Acronym gee (old: xic)
Name hexacontitetrapeton,
hexacross6),
aeroex(id),
hexateral antiprism,
vertex figure of zee,
Gosset polytope 31,1
Circumradius 1/sqrt(2) = 0.707107
Inradius 1/sqrt(12) = 0.288675
Lace city
in approx. ASCII-art
o3o3o3o   x3o3o3o   
                    
                    
                    
                    
   o3o3o3x   o3o3o3o
x o3o3o   o x3o3o  
                   
                   
                   
                   
                   
  o o3o3x   x o3o3o
x3o o3o   o3o x3o
                 
                 
                 
                 
                 
                 
o3o o3x   o3x o3o
 ©  
o3o3o *b3o       o3o3o *b3o
                           
                           
                           
                           
                           
         x3o3o *b3o        
                           
                           
                           
                           
                           
o3o3o *b3o       o3o3o *b3o
Coordinates (1/sqrt(2), 0, 0, 0, 0, 0)   & all permutations, all changes of sign
Volume 1/90 = 0.011111
Surface 2 sqrt(3)/15 = 0.230940
Rel. Roundness 5 π3/576 = 26.915171 %
Dual ax
Dihedral angles
  • at pen between hix and hix:   arccos(-2/3) = 131.810315°
Confer
related segmentopeta:
tacpy   hexasc   octete   squepe  
general polytopal classes:
orthoplex   noble polytopes   segmentopeta   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

x3o3o3o3o4o

. . . . . . | 12  10 |  40 |  80 |  80 | 32
------------+----+----+-----+-----+-----+---
x . . . . . |  2 | 60    8 |  24 |  32 | 16
------------+----+----+-----+-----+-----+---
x3o . . . . |  3 |  3 | 160    6 |  12 |  8
------------+----+----+-----+-----+-----+---
x3o3o . . .   4 |  6 |   4 | 240 |   4 |  4
------------+----+----+-----+-----+-----+---
x3o3o3o . .   5 | 10 |  10 |   5 | 192 |  2
------------+----+----+-----+-----+-----+---
x3o3o3o3o .   6 | 15 |  20 |  15 |   6 | 64

x3o3o3o3o4/3o

. . . . .   . | 12  10 |  40 |  80 |  80 | 32
--------------+----+----+-----+-----+-----+---
x . . . .   . |  2 | 60    8 |  24 |  32 | 16
--------------+----+----+-----+-----+-----+---
x3o . . .   . |  3 |  3 | 160    6 |  12 |  8
--------------+----+----+-----+-----+-----+---
x3o3o . .   .   4 |  6 |   4 | 240 |   4 |  4
--------------+----+----+-----+-----+-----+---
x3o3o3o .   .   5 | 10 |  10 |   5 | 192 |  2
--------------+----+----+-----+-----+-----+---
x3o3o3o3o   .   6 | 15 |  20 |  15 |   6 | 64

o3o3o *b3o3o3x

. . .    . . . | 12  10 |  40 |  80 |  80 | 16 16
---------------+----+----+-----+-----+-----+------
. . .    . . x |  2 | 60    8 |  24 |  32 |  8  8
---------------+----+----+-----+-----+-----+------
. . .    . o3x |  3 |  3 | 160    6 |  12 |  4  4
---------------+----+----+-----+-----+-----+------
. . .    o3o3x   4 |  6 |   4 | 240 |   4 |  2  2
---------------+----+----+-----+-----+-----+------
. o . *b3o3o3x   5 | 10 |  10 |   5 | 192 |  1  1
---------------+----+----+-----+-----+-----+------
o3o . *b3o3o3x   6 | 15 |  20 |  15 |   6 | 32  *
. o3o *b3o3o3x   6 | 15 |  20 |  15 |   6 |  * 32

xo3oo3oo3oo3ox&#x   → height = 1/sqrt(3) = 0.577350
(hix || inv hix)

o.3o.3o.3o.3o.     & | 12   5  5 | 10  30 | 10  40 30 |  5 25  50 | 1  6 15 10
---------------------+----+-------+--------+-----------+-----------+-----------
x. .. .. .. ..     & |  2 | 30  *   4   4 |  6  12  6 |  4 12  16 | 1  4  7  4
oo3oo3oo3oo3oo&#x    |  2 |  * 30   0   8 |  0  12 12 |  0  8  24 | 0  2  8  6
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o. .. .. ..     & |  3 |  3  0 | 40   *   3   3  0 |  3  6   3 | 1  3  3  1
xo .. .. .. ..&#x  & |  3 |  1  2 |  * 120   0   3  3 |  0  3   9 | 0  1  4  3
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o. .. ..     &   4 |  6  0 |  4   0 | 30   *  * |  2  2   0 | 1  2  1  0
xo3oo .. .. ..&#x  &   4 |  3  3 |  1   3 |  * 120  * |  0  2   2 | 0  1  2  1
xo .. .. .. ox&#x      4 |  2  4 |  0   4 |  *   * 90 |  0  0   4 | 0  0  2  2
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o.3o. ..     &   5 | 10  0 | 10   0 |  5   0  0 | 12  *   * | 1  1  0  0
xo3oo3oo .. ..&#x  &   5 |  6  4 |  4   6 |  1   4  0 |  * 60   * | 0  1  1  0
xo3oo .. .. ox&#x  &   5 |  4  6 |  1   9 |  0   2  3 |  *  * 120 | 0  0  1  1
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o.3o.3o.     &   6 | 15  0 | 20   0 | 15   0  0 |  6  0   0 | 2  *  *  *
xo3oo3oo3oo ..&#x  &   6 | 10  5 | 10  10 |  5  10  0 |  1  5   0 | * 12  *  *
xo3oo3oo .. ox&#x  &   6 |  7  8 |  4  16 |  1   8  6 |  0  2   4 | *  * 30  *
xo3oo .. oo3ox&#x      6 |  6  9 |  2  18 |  0   6  9 |  0  0   6 | *  *  * 20

oxo3ooo3ooo3ooo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(pt || pseudo tac || pt)

o..3o..3o..3o..4o..     & | 2  *  10  0 | 40  0 |  80  0 |  80  0 | 32
.o.3.o.3.o.3.o.4.o.       | * 10   2  8 | 16 24 |  48 32 |  64 16 | 32
--------------------------+------+-------+-------+--------+--------+---
oo.3oo.3oo.3oo.4oo.&#x  & | 1  1 | 20  *   8  0 |  24  0 |  32  0 | 16
.x. ... ... ... ...       | 0  2 |  * 40   2  6 |  12 12 |  24  8 | 16
--------------------------+------+-------+-------+--------+--------+---
ox. ... ... ... ...&#x  & | 1  2 |  2  1 | 80  *    6  0 |  12  0 |  8
.x.3.o. ... ... ...       | 0  3 |  0  3 |  * 80    2  4 |   8  4 |  8
--------------------------+------+-------+-------+--------+--------+---
ox.3oo. ... ... ...&#x  &  1  3 |  3  3 |  3  1 | 160  * |   4  0 |  4
.x.3.o.3.o. ... ...        0  4 |  0  6 |  0  4 |   * 80 |   2  2 |  4
--------------------------+------+-------+-------+--------+--------+---
ox.3oo.3oo. ... ...&#x  &  1  4 |  4  6 |  6  4 |   4  1 | 160  * |  2
.x.3.o.3.o.3.o. ...        0  5 |  0 10 |  0 10 |   0  5 |   * 32 |  2
--------------------------+------+-------+-------+--------+--------+---
ox.3oo.3oo.3oo. ...&#x  &  1  5 |  5 10 | 10 10 |  10  5 |   5  1 | 64

qo ox3oo3oo3oo4oo&#zx   → height = 0
(tegum sum of q-line and perp tac)
(tegum product of q-line with tac)

o. o.3o.3o.3o.4o.    | 2  *  10  0 | 40  0 |  80  0 |  80  0 | 32
.o .o3.o3.o3.o4.o    | * 10   2  8 | 16 24 |  48 32 |  64 16 | 32
---------------------+------+-------+-------+--------+--------+---
oo oo3oo3oo3oo4oo&#x | 1  1 | 20  *   8  0 |  24  0 |  32  0 | 16
.. .x .. .. .. ..    | 0  2 |  * 40   2  6 |  12 12 |  24  8 | 16
---------------------+------+-------+-------+--------+--------+---
.. ox .. .. .. ..&#x | 1  2 |  2  1 | 80  *    6  0 |  12  0 |  8
.. .x3.o .. .. ..    | 0  3 |  0  3 |  * 80    2  4 |   8  4 |  8
---------------------+------+-------+-------+--------+--------+---
.. ox3oo .. .. ..&#x  1  3 |  3  3 |  3  1 | 160  * |   4  0 |  4
.. .x3.o3.o .. ..     0  4 |  0  6 |  0  4 |   * 80 |   2  2 |  4
---------------------+------+-------+-------+--------+--------+---
.. ox3oo3oo .. ..&#x  1  4 |  4  6 |  6  4 |   4  1 | 160  * |  2
.. .x3.o3.o3.o ..     0  5 |  0 10 |  0 10 |   0  5 |   * 32 |  2
---------------------+------+-------+-------+--------+--------+---
.. ox3oo3oo3oo ..&#x  1  5 |  5 10 | 10 10 |  10  5 |   5  1 | 64

ooo3ooo3ooo *b3ooo3oxo&#xt   → both heights = 1/sqrt(2) = 0.707107
(pt || pseudo tac || pt)

o..3o..3o.. *b3o..3o..     & | 2  *  10  0 | 40  0 |  80  0 |  80  0  0 | 16 16
.o.3.o.3.o. *b3.o.3.o.       | * 10   2  8 | 16 24 |  48 32 |  64  8  8 | 16 16
-----------------------------+------+-------+-------+--------+-----------+------
oo.3oo.3oo. *b3oo.3oo.&#x  & | 1  1 | 20  *   8  0 |  24  0 |  32  0  0 |  8  8
... ... ...    ... .x.       | 0  2 |  * 40   2  6 |  12 12 |  24  4  4 |  8  8
-----------------------------+------+-------+-------+--------+-----------+------
... ... ...    ... ox.&#x  & | 1  2 |  2  1 | 80  *    6  0 |  12  0  0 |  4  4
... ... ...    .o.3.x.       | 0  3 |  0  3 |  * 80    2  4 |   8  2  2 |  4  4
-----------------------------+------+-------+-------+--------+-----------+------
... ... ...    oo.3ox.&#x  &  1  3 |  3  3 |  3  1 | 160  * |   4  0  0 |  2  2
... .o. ... *b3.o.3.x.        0  4 |  0  6 |  0  4 |   * 80 |   2  1  1 |  2  2
-----------------------------+------+-------+-------+--------+-----------+------
... oo. ... *b3oo.3ox.&#x  &  1  4 |  4  6 |  6  4 |   4  1 | 160  *  * |  1  1
.o.3.o. ... *b3.o.3.x.        0  5 |  0 10 |  0 10 |   0  5 |   * 16  * |  2  0
... .o.3.o. *b3.o.3.x.        0  5 |  0 10 |  0 10 |   0  5 |   *  * 16 |  0  2
-----------------------------+------+-------+-------+--------+-----------+------
oo.3oo. ... *b3oo.3ox.&#x  &  1  5 |  5 10 | 10 10 |  10  5 |   5  1  0 | 32  *
... oo.3oo. *b3oo.3ox.&#x  &  1  5 |  5 10 | 10 10 |  10  5 |   5  0  1 |  * 32

qo oo3oo3oo *c3oo3ox&#zx   → height = 0
(tegum sum of q-line and perp tac)
(tegum product of q-line with tac)

o. o.3o.3o. *c3o.3o.    | 2  *  10  0 | 40  0 |  80  0 |  80  0  0 | 16 16
.o .o3.o3.o *c3.o3.o    | * 10   2  8 | 16 24 |  48 32 |  64  8  8 | 16 16
------------------------+------+-------+-------+--------+-----------+------
oo oo3oo3oo *c3oo3oo&#x | 1  1 | 20  *   8  0 |  24  0 |  32  0  0 |  8  8
.. .. .. ..    .. .x    | 0  2 |  * 40   2  6 |  12 12 |  24  4  4 |  8  8
------------------------+------+-------+-------+--------+-----------+------
.. .. .. ..    .. ox&#x | 1  2 |  2  1 | 80  *    6  0 |  12  0  0 |  4  4
.. .. .. ..    .o3.x    | 0  3 |  0  3 |  * 80    2  4 |   8  2  2 |  4  4
------------------------+------+-------+-------+--------+-----------+------
.. .. .. ..    oo3ox&#x  1  3 |  3  3 |  3  1 | 160  * |   4  0  0 |  2  2
.. .. .o .. *c3.o3.x     0  4 |  0  6 |  0  4 |   * 80 |   2  1  1 |  2  2
------------------------+------+-------+-------+--------+-----------+------
.. .. oo .. *c3oo3ox&#x  1  4 |  4  6 |  6  4 |   4  1 | 160  *  * |  1  1
.. .o3.o .. *c3.o3.x     0  5 |  0 10 |  0 10 |   0  5 |   * 16  * |  2  0
.. .. .o3.o *c3.o3.x     0  5 |  0 10 |  0 10 |   0  5 |   *  * 16 |  0  2
------------------------+------+-------+-------+--------+-----------+------
.. oo3oo .. *c3oo3ox&#x  1  5 |  5 10 | 10 10 |  10  5 |   5  1  0 | 32  *
.. .. oo3oo *c3oo3ox&#x  1  5 |  5 10 | 10 10 |  10  5 |   5  0  1 |  * 32

oxoo3oooo3oooo3ooox&#xr   → all heights = sqrt(3/5) = 0.774597
(pt || (pseudo pen || pseudo inv pen) || pt)

o(..).3o(..).3o(..).3o(..).     & | 2  *   5  5  0  0 | 10 10 20  0  0 | 10 10 30 30  0  0  0 |  5  5 20 30 20 0  0  0 | 1 1  5 10 10  5
.(o.).3.(o.).3.(o.).3.(o.).     & | * 10   1  1  4  4 |  4  4  8  6 18 |  6  6 18 18  4 16 12 |  4  4 16 24 16 1  5 10 | 1 1  5 10 10  5
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(o.).3o(o.).3o(o.).3o(o.).&#x  & | 1  1 | 10  *  *  *   4  0  4  0  0 |  6  0 12  6  0  0  0 |  4  0 12 12  4 0  0  0 | 1 0  4  6  4  1
o(.o).3o(.o).3o(.o).3o(.o).&#x  & | 1  1 |  * 10  *  *   0  4  4  0  0 |  0  6  6 12  0  0  0 |  0  4  4 12 12 0  0  0 | 0 1  1  4  6  4
.(x.). .(..). .(..). .(..).     & | 0  2 |  *  * 20  *   1  1  0  3  3 |  3  3  3  3  3  6  3 |  3  3  6  6  6 1  3  4 | 1 1  3  4  4  3
.(oo).3.(oo).3.(oo).3.(oo).&#x    | 0  2 |  *  *  * 20   0  0  2  0  6 |  0  0  6  6  0  6  6 |  0  0  6 12  6 0  2  6 | 0 0  2  6  6  2
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(x.). .(..). .(..). .(..).&#x  & | 1  2 |  2  0  1  0 | 20  *  *  *  *   3  0  3  0  0  0  0 |  3  0  6  3  0 0  0  0 | 1 0  3  3  1  0
.(..). .(..). .(..). o(.x).&#x  & | 1  2 |  0  2  1  0 |  * 20  *  *  *   0  3  0  3  0  0  0 |  0  3  0  3  6 0  0  0 | 0 1  0  1  3  3
o(oo).3o(oo).3o(oo).3o(oo).&#x  & | 1  2 |  1  1  0  1 |  *  * 40  *  *   0  0  3  3  0  0  0 |  0  0  3  6  3 0  0  0 | 0 0  1  3  3  1
.(x.).3.(o.). .(..). .(..).     & | 0  3 |  0  0  3  0 |  *  *  * 20  *   1  1  0  0  2  2  0 |  2  2  2  0  2 1  2  1 | 1 1  2  1  1  2
.(xo). .(..). .(..). .(..).&#x  & | 0  3 |  0  0  1  2 |  *  *  *  * 60   0  0  1  1  0  2  2 |  0  0  2  4  2 0  1  3 | 0 0  1  3  3  1
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(x.).3o(o.). .(..). .(..).&#x  &  1  3 |  3  0  3  0 |  3  0  0  1  0 | 20  *  *  *  *  *  * |  2  0  2  0  0 0  0  0 | 1 0  2  1  0  0
.(..). .(..). o(.o).3o(.x).&#x  &  1  3 |  0  3  3  0 |  0  3  0  1  0 |  * 20  *  *  *  *  * |  0  2  0  0  2 0  0  0 | 0 1  0  0  1  2
o(xo). .(..). .(..). .(..).&#x  &  1  3 |  2  1  1  2 |  1  0  2  0  1 |  *  * 60  *  *  *  * |  0  0  2  2  0 0  0  0 | 0 0  1  2  1  0
.(..). .(..). .(..). o(ox).&#x  &  1  3 |  1  2  1  2 |  0  1  2  0  1 |  *  *  * 60  *  *  * |  0  0  0  2  2 0  0  0 | 0 0  0  1  2  1
.(x.).3.(o.).3.(o.). .(..).     &  0  4 |  0  0  6  0 |  0  0  0  4  0 |  *  *  *  * 10  *  * |  1  1  0  0  0 1  1  0 | 1 1  1  0  0  1
.(xo).3.(oo). .(..). .(..).&#x  &  0  4 |  0  0  3  3 |  0  0  0  1  3 |  *  *  *  *  * 40  * |  0  0  1  0  1 0  1  1 | 0 0  1  1  1  1
.(xo). .(..). .(..). .(ox).&#x     0  4 |  0  0  2  4 |  0  0  0  0  4 |  *  *  *  *  *  * 30 |  0  0  0  2  0 0  0  2 | 0 0  0  2  2  0
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(x.).3o(o.).3o(o.). .(..).&#x  &  1  4 |  4  0  6  0 |  6  0  0  4  0 |  4  0  0  0  1  0  0 | 10  *  *  *  * *  *  * | 1 0  1  0  0  0
.(..). o(.o).3o(.o).3o(.x).&#x  &  1  4 |  0  4  6  0 |  0  6  0  4  0 |  0  4  0  0  1  0  0 |  * 10  *  *  * *  *  * | 0 1  0  0  0  1
o(xo).3o(oo). .(..). .(..).&#x  &  1  4 |  3  1  3  3 |  3  0  3  1  3 |  1  0  3  0  0  1  0 |  *  * 40  *  * *  *  * | 0 0  1  1  0  0
o(xo). .(..). .(..). o(ox).&#x  &  1  4 |  2  2  2  4 |  1  1  4  0  4 |  0  0  2  2  0  0  1 |  *  *  * 60  * *  *  * | 0 0  0  1  1  0
.(..). .(..). o(oo).3o(ox).&#x  &  1  4 |  1  3  3  3 |  0  3  3  1  3 |  0  1  0  3  0  1  0 |  *  *  *  * 40 *  *  * | 0 0  0  0  1  1
.(x.).3.(o.).3.(o.).3.(o.).     &  0  5 |  0  0 10  0 |  0  0  0 10  0 |  0  0  0  0  5  0  0 |  *  *  *  *  * 2  *  * | 1 1  0  0  0  0
.(xo).3.(oo).3.(oo). .(..).&#x  &  0  5 |  0  0  6  4 |  0  0  0  4  6 |  0  0  0  0  1  4  0 |  *  *  *  *  * * 10  * | 0 0  1  0  0  1
.(xo).3.(oo). .(..). .(ox).&#x  &  0  5 |  0  0  4  6 |  0  0  0  1  9 |  0  0  0  0  0  2  3 |  *  *  *  *  * *  * 20 | 0 0  0  1  1  0
----------------------------------+------+-------------+----------------+----------------------+------------------------+----------------
o(x.).3o(o.).3o(o.).3o(o.).&#x  &  1  5 |  5  0 10  0 | 10  0  0 10  0 | 10  0  0  0  5  0  0 |  5  0  0  0  0 1  0  0 | 2 *  *  *  *  *
o(.o).3o(.o).3o(.o).3o(.x).&#x  &  1  5 |  0  5 10  0 |  0 10  0 10  0 |  0 10  0  0  5  0  0 |  0  5  0  0  0 1  0  0 | * 2  *  *  *  *
o(xo).3o(oo).3o(oo). .(..).&#x  &  1  5 |  4  1  6  4 |  6  0  4  4  6 |  4  0  6  0  1  4  0 |  1  0  4  0  0 0  1  0 | * * 10  *  *  *
o(xo).3o(oo). .(..). o(ox).&#x  &  1  5 |  3  2  4  6 |  3  1  6  1  9 |  1  0  6  3  0  2  3 |  0  0  2  3  0 0  0  1 | * *  * 20  *  *
o(xo). .(..). o(oo).3o(ox).&#x  &  1  5 |  2  3  4  6 |  1  3  6  1  9 |  0  1  3  6  0  2  3 |  0  0  0  3  2 0  0  1 | * *  *  * 20  *
.(..). o(oo).3o(oo).3o(ox).&#x  &  1  5 |  1  4  6  4 |  0  6  4  4  6 |  0  4  0  6  1  4  0 |  0  1  0  0  4 0  1  0 | * *  *  *  * 10

oqo xoo3ooo3ooo3oox&#xt   → both heights = 1/sqrt(10) = 0.316228
(pen || perp pseudo q-line || dual pen)

o.. o..3o..3o..3o..    | 5 * *   4  2  4  0  0 |  6  8 12  6  8  0  0 | 4 12 12 12  4 24 12  0 0 | 1  8 4  6  4 1 24 24  8  0 0 | 2  8 12  8  2 0
.o. .o.3.o.3.o.3.o.    | * 2 *   0  5  0  5  0 |  0 10  0  0 20 10  0 | 0 10  0  0  0 30 30 10 0 | 0  5 0  0  0 0 20 30 20  5 0 | 1  5 10 10  5 1
..o ..o3..o3..o3..o    | * * 5   0  0  4  2  4 |  0  0  6 12  8  8  6 | 0  0  4 12 12 12 24 12 4 | 0  0 1  4  6 4  8 24 24  8 1 | 0  2  8 12  8 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... x.. ... ... ...    | 2 0 0 | 10  *  *  *  *   3  2  3  0  0  0  0 | 3  6  6  3  0  6  0  0 0 | 1  6 3  3  1 0 12  6  0  0 0 | 2  6  6  2  0 0
oo. oo.3oo.3oo.3oo.&#x | 1 1 0 |  * 10  *  *  *   0  4  0  0  4  0  0 | 0  6  0  0  0 12  6  0 0 | 0  4 0  0  0 0 12 12  4  0 0 | 1  4  6  4  1 0
o.o o.o3o.o3o.o3o.o&#x | 1 0 1 |  *  * 20  *  *   0  0  3  3  2  0  0 | 0  0  3  6  3  6  6  0 0 | 0  0 1  3  3 1  6 12  6  0 0 | 0  2  6  6  2 0
.oo .oo3.oo3.oo3.oo&#x | 0 1 1 |  *  *  * 10  *   0  0  0  0  4  4  0 | 0  0  0  0  0  6 12  6 0 | 0  0 0  0  0 0  4 12 12  4 0 | 0  1  4  6  4 1
... ... ... ... ..x    | 0 0 2 |  *  *  *  * 10   0  0  0  3  0  2  3 | 0  0  0  3  6  0  6  6 3 | 0  0 0  1  3 3  0  6 12  6 1 | 0  0  2  6  6 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... x..3o.. ... ...    | 3 0 0 |  3  0  0  0  0 | 10  *  *  *  *  *  *  2  2  2  0  0  0  0  0 0 | 1  4 2  1  0 0  4  0  0  0 0 | 2  4  2  0  0 0
... xo. ... ... ...&#x | 2 1 0 |  1  2  0  0  0 |  * 20  *  *  *  *  *  0  3  0  0  0  3  0  0 0 | 0  3 0  0  0 0  6  3  0  0 0 | 1  3  3  1  0 0
... x.o ... ... ...&#x | 2 0 1 |  1  0  2  0  0 |  *  * 30  *  *  *  *  0  0  3  3  0  2  0  0 0 | 0  0 1  2  1 0  4  4  0  0 0 | 0  2  4  2  0 0
... ... ... ... o.x&#x | 1 0 2 |  0  0  2  0  1 |  *  *  * 30  *  *  *  0  0  0  2  2  0  2  0 0 | 0  0 0  1  2 1  0  4  4  0 0 | 0  0  2  4  2 0
ooo ooo3ooo3ooo3ooo&#x | 1 1 1 |  0  1  1  1  0 |  *  *  *  * 40  *  *  0  0  0  0  0  3  3  0 0 | 0  0 0  0  0 0  3  6  3  0 0 | 0  1  3  3  1 0
... ... ... ... .ox&#x | 0 1 2 |  0  0  0  2  1 |  *  *  *  *  * 20  *  0  0  0  0  0  0  3  3 0 | 0  0 0  0  0 0  0  3  6  3 0 | 0  0  1  3  3 1
... ... ... ..o3..x    | 0 0 3 |  0  0  0  0  3 |  *  *  *  *  *  * 10  0  0  0  0  2  0  0  2 2 | 0  0 0  0  1 2  0  0  4  4 1 | 0  0  0  2  4 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... x..3o..3o.. ...     4 0 0 |  6  0  0  0  0 |  4  0  0  0  0  0  0 | 5  *  *  *  *  *  *  * * | 1  2 1  0  0 0  0  0  0  0 0 | 2  2  0  0  0 0
... xo.3oo. ... ...&#x  3 1 0 |  3  3  0  0  0 |  1  3  0  0  0  0  0 | * 20  *  *  *  *  *  * * | 0  2 0  0  0 0  2  0  0  0 0 | 1  2  1  0  0 0
... x.o3o.o ... ...&#x  3 0 1 |  3  0  3  0  0 |  1  0  3  0  0  0  0 | *  * 20  *  *  *  *  * * | 0  0 1  1  0 0  2  0  0  0 0 | 0  2  2  0  0 0
... x.o ... ... o.x&#x  2 0 2 |  1  0  4  0  1 |  0  0  2  2  0  0  0 | *  *  * 30  *  *  *  * * | 0  0 0  1  1 0  0  2  0  0 0 | 0  0  2  2  0 0
... ... ... o.o3o.x&#x  1 0 3 |  0  0  3  0  3 |  0  0  0  3  0  0  1 | *  *  *  * 20  *  *  * * | 0  0 0  0  1 1  0  0  2  0 0 | 0  0  0  2  2 0
... xoo ... ... ...&#x  2 1 1 |  1  2  2  1  0 |  0  1  1  0  2  0  0 | *  *  *  *  * 60  *  * * | 0  0 0  0  0 0  2  2  0  0 0 | 0  1  2  1  0 0
... ... ... ... oox&#x  1 1 2 |  0  1  2  2  1 |  0  0  0  1  2  1  0 | *  *  *  *  *  * 60  * * | 0  0 0  0  0 0  0  2  2  0 0 | 0  0  1  2  1 0
... ... ... .oo3.ox&#x  0 1 3 |  0  0  0  3  3 |  0  0  0  0  0  3  1 | *  *  *  *  *  *  * 20 * | 0  0 0  0  0 0  0  0  2  2 0 | 0  0  0  1  2 1
... ... ..o3..o3..x     0 0 4 |  0  0  0  0  6 |  0  0  0  0  0  0  4 | *  *  *  *  *  *  *  * 5 | 0  0 0  0  0 1  0  0  0  2 1 | 0  0  0  0  2 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... x..3o..3o..3o..     5 0 0 | 10  0  0  0  0 | 10  0  0  0  0  0  0 | 5  0  0  0  0  0  0  0 0 | 1  * *  *  * *  *  *  *  * * | 2  0  0  0  0 0
... xo.3oo.3oo. ...&#x  4 1 0 |  6  4  0  0  0 |  4  6  0  0  0  0  0 | 1  4  0  0  0  0  0  0 0 | * 10 *  *  * *  *  *  *  * * | 1  1  0  0  0 0
... x.o3o.o3o.o ...&#x  4 0 1 |  6  0  4  0  0 |  4  0  6  0  0  0  0 | 1  0  4  0  0  0  0  0 0 | *  * 5  *  * *  *  *  *  * * | 0  2  0  0  0 0
... x.o3o.o ... o.x&#x  3 0 2 |  3  0  6  0  1 |  1  0  6  3  0  0  0 | 0  0  2  3  0  0  0  0 0 | *  * * 10  * *  *  *  *  * * | 0  0  2  0  0 0
... x.o ... o.o3o.x&#x  2 0 3 |  1  0  6  0  3 |  0  0  3  6  0  0  1 | 0  0  0  3  2  0  0  0 0 | *  * *  * 10 *  *  *  *  * * | 0  0  0  2  0 0
... ... o.o3o.o3o.x&#x  1 0 4 |  0  0  4  0  6 |  0  0  0  6  0  0  4 | 0  0  0  0  4  0  0  0 1 | *  * *  *  * 5  *  *  *  * * | 0  0  0  0  2 0
... xoo3ooo ... ...&#x  3 1 1 |  3  3  3  1  0 |  1  3  3  0  3  0  0 | 0  1  1  0  0  3  0  0 0 | *  * *  *  * * 40  *  *  * * | 0  1  1  0  0 0
... xoo ... ... oox&#x  2 1 2 |  1  2  4  2  1 |  0  1  2  2  4  1  0 | 0  0  0  1  0  2  2  0 0 | *  * *  *  * *  * 60  *  * * | 0  0  1  1  0 0
... ... ... ooo3oox&#x  1 1 3 |  0  1  3  3  3 |  0  0  0  3  3  3  1 | 0  0  0  0  1  0  3  1 0 | *  * *  *  * *  *  * 40  * * | 0  0  0  1  1 0
... ... .oo3.oo3.ox&#x  0 1 4 |  0  0  0  4  6 |  0  0  0  0  0  6  4 | 0  0  0  0  0  0  0  4 1 | *  * *  *  * *  *  *  * 10 * | 0  0  0  0  1 1
... ..o3..o3..o3..x     0 0 5 |  0  0  0  0 10 |  0  0  0  0  0  0 10 | 0  0  0  0  0  0  0  0 5 | *  * *  *  * *  *  *  *  * 1 | 0  0  0  0  0 2
-----------------------+-------+----------------+----------------------+--------------------------+------------------------------+----------------
... xo.3oo.3oo.3oo.&#x  5 1 0 | 10  5  0  0  0 | 10 10  0  0  0  0  0 | 5 10  0  0  0  0  0  0 0 | 1  5 0  0  0 0  0  0  0  0 0 | 2  *  *  *  * *
... xoo3ooo3ooo ...&#x  4 1 1 |  6  4  4  1  0 |  4  6  6  0  4  0  0 | 1  4  4  0  0  6  0  0 0 | 0  1 1  0  0 0  4  0  0  0 0 | * 10  *  *  * *
... xoo3ooo ... oox&#x  3 1 2 |  3  3  6  2  1 |  1  3  6  3  6  1  0 | 0  1  2  3  0  6  3  0 0 | 0  0 0  1  0 0  2  3  0  0 0 | *  * 20  *  * *
... xoo ... ooo3oox&#x  2 1 3 |  1  2  6  3  3 |  0  1  3  6  6  3  1 | 0  0  0  3  2  3  6  1 0 | 0  0 0  0  1 0  0  3  2  0 0 | *  *  * 20  * *
... ... ooo3ooo3oox&#x  1 1 4 |  0  1  4  4  6 |  0  0  0  6  4  6  4 | 0  0  0  0  4  0  6  4 1 | 0  0 0  0  0 1  0  0  4  1 0 | *  *  *  * 10 *
... .oo3.oo3.oo3.ox&#x  0 1 5 |  0  0  0  5 10 |  0  0  0  0  0 10 10 | 0  0  0  0  0  0  0 10 5 | 0  0 0  0  0 0  0  0  0  5 1 | *  *  *  *  * 2

xox oxo3ooo3ooo4ooo&#xt   → both heights = 1/2
(line || pseudo perp hex || line)

o.. o..3o..3o..4o..     & | 4 *  1  8 1  0 |  8 24  8  0 | 24  32 24  0 | 32 16 32 | 16 16
.o. .o.3.o.3.o.4.o.       | * 8  0  4 0  6 |  2 24  2 12 | 12  48 12  8 | 24 32 24 | 16 16
--------------------------+-----+-----------+-------------+--------------+----------+------
x.. ... ... ... ...     & | 2 0 | 2  * *  *   8  0  0  0 | 24   0  0  0 | 32  0  0 | 16  0
oo. oo.3oo.3oo.4oo.&#x  & | 1 1 | * 32 *  *   1  6  1  0 |  6  12  6  0 | 12  8 12 |  8  8
o.o o.o3o.o3o.o4o.o&#x    | 2 0 | *  * 2  *   0  0  8  0 |  0   0 24  0 |  0  0 32 |  0 16
... .x. ... ... ...       | 0 2 | *  * * 24   0  4  0  4 |  2  16  2  4 |  8 16  8 |  8  8
--------------------------+-----+-----------+-------------+--------------+----------+------
xo. ... ... ... ...&#x  & | 2 1 | 1  2 0  0 | 16  *  *  *   8   0  0  0 | 12  0  0 |  8  0
... ox. ... ... ...&#x  & | 1 2 | 0  2 0  1 |  * 96  *  *   1   4  1  0 |  4  4  4 |  4  4
ooo ooo3ooo3ooo4ooo&#x    | 2 1 | 0  2 1  0 |  *  * 16  *   0   0  6  0 |  0  0 12 |  0  8
... .x.3.o. ... ...       | 0 3 | 0  0 0  3 |  *  *  * 32   0   4  0  2 |  2  8  2 |  4  4
--------------------------+-----+-----------+-------------+--------------+----------+------
xo. ox. ... ... ...&#x  &  2 2 | 1  4 0  1 |  2  2  0  0 | 48   *  *  * |  4  0  0 |  4  0
... ox.3oo. ... ...&#x  &  1 3 | 0  3 0  3 |  0  3  0  1 |  * 128  *  * |  1  2  1 |  2  2
... oxo ... ... ...&#x     2 2 | 0  4 1  1 |  0  2  2  0 |  *   * 48  * |  0  0  4 |  0  4
... .x.3.o.3.o. ...        0 4 | 0  0 0  6 |  0  0  0  4 |  *   *  * 16 |  0  4  0 |  2  2
--------------------------+-----+-----------+-------------+--------------+----------+------
xo. ox.3oo. ... ...&#x  &  2 3 | 1  6 0  3 |  3  6  0  1 |  3   2  0  0 | 64  *  * |  2  0
... ox.3oo.3oo. ...&#x  &  1 4 | 0  4 0  6 |  0  6  0  4 |  0   4  0  1 |  * 64  * |  1  1
... oxo3ooo ... ...&#x     2 3 | 0  6 1  3 |  0  6  3  1 |  0   2  3  0 |  *  * 64 |  0  2
--------------------------+-----+-----------+-------------+--------------+----------+------
xo. ox.3oo.3oo. ...&#x  &  2 4 | 1  8 0  6 |  4 12  0  4 |  6   8  0  1 |  4  2  0 | 32  *
... oxo3ooo3ooo ...&#x     2 4 | 0  8 1  6 |  0 12  4  4 |  0   8  6  1 |  0  2  4 |  * 32

ooo3ooo3ooo *b3oxo xox&#xt   → both heights = 1/2
(line || pseudo perp hex || line)

o..3o..3o.. *b3o.. o..     & | 4 *  1  8 1  0 | 24  8  8  0 |  32 24 24 0 0 |  8  8 32 32 |  8  8  8  8
.o.3.o.3.o. *b3.o. .o.       | * 8  0  4 0  6 | 24  2  2 12 |  48 12 12 4 4 | 16 16 24 24 |  8  8  8  8
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
... ... ...    ... x..     & | 2 0 | 2  * *  *   0  8  0  0 |   0 24  0 0 0 |  0  0 32  0 |  8  8  0  0
oo.3oo.3oo. *b3oo. oo.&#x  & | 1 1 | * 32 *  *   6  1  1  0 |  12  6  6 0 0 |  4  4 12 12 |  4  4  4  4
o.o3o.o3o.o *b3o.o o.o&#x    | 2 0 | *  * 2  *   0  0  8  0 |   0  0 24 0 0 |  0  0  0 32 |  0  0  8  8
... ... ...    .x. ...       | 0 2 | *  * * 24   4  0  0  4 |  16  2  2 2 2 |  8  8  8  8 |  4  4  4  4
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
... ... ...    ox. ...&#x  & | 1 2 | 0  2 0  1 | 96  *  *  *    4  1  1 0 0 |  2  2  4  4 |  2  2  2  2
... ... ...    ... xo.&#x  & | 2 1 | 1  2 0  0 |  * 16  *  *    0  6  0 0 0 |  0  0 12  0 |  4  4  0  0
ooo3ooo3ooo *b3ooo ooo&#x    | 2 1 | 0  2 1  0 |  *  * 16  *    0  0  6 0 0 |  0  0  0 12 |  0  0  4  4
... .o. ... *b3.x. ...       | 0 3 | 0  0 0  3 |  *  *  * 32    4  0  0 1 1 |  4  4  2  2 |  2  2  2  2
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
... oo. ... *b3ox. ...&#x  &  1 3 | 0  3 0  3 |  3  0  0  1 | 128  *  * * * |  1  1  1  1 |  1  1  1  1
... ... ...    ox. xo.&#x  &  2 2 | 1  4 0  1 |  2  2  0  0 |   * 48  * * * |  0  0  4  0 |  2  2  0  0
... ... ...    oxo ...&#x     2 2 | 0  4 1  1 |  2  0  2  0 |   *  * 48 * * |  0  0  0  4 |  0  0  2  2
.o.3.o. ... *b3.x. ...        0 4 | 0  0 0  6 |  0  0  0  4 |   *  *  * 8 * |  4  0  0  0 |  2  0  2  0
... .o.3.o. *b3.x. ...        0 4 | 0  0 0  6 |  0  0  0  4 |   *  *  * * 8 |  0  4  0  0 |  0  2  0  2
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
oo.3oo. ... *b3ox. ...&#x  &  1 4 | 0  4 0  6 |  6  0  0  4 |   4  0  0 1 0 | 32  *  *  * |  1  0  1  0
... oo.3oo. *b3ox. ...&#x  &  1 4 | 0  4 0  6 |  6  0  0  4 |   4  0  0 0 1 |  * 32  *  * |  0  1  0  1
... oo. ... *b3ox. xo.&#x  &  2 3 | 1  6 0  3 |  6  3  0  1 |   2  3  0 0 0 |  *  * 64  * |  1  1  0  0
... ooo ... *b3oxo ...&#x     2 3 | 0  6 1  3 |  6  0  3  1 |   2  0  3 0 0 |  *  *  * 64 |  0  0  1  1
-----------------------------+-----+-----------+-------------+---------------+-------------+------------
oo.3oo. ... *b3ox. xo.&#x  &  2 4 | 1  8 0  6 | 12  4  0  4 |   8  6  0 1 0 |  2  0  4  0 | 16  *  *  *
... oo.3oo. *b3ox. xo.&#x  &  2 4 | 1  8 0  6 | 12  4  0  4 |   8  6  0 0 1 |  0  2  4  0 |  * 16  *  *
ooo3ooo ... *b3oxo ...&#x     2 4 | 0  8 1  6 | 12  0  4  4 |   8  0  6 1 0 |  2  0  0  4 |  *  * 16  *
... ooo3ooo *b3oxo ...&#x     2 4 | 0  8 1  6 | 12  0  4  4 |   8  0  6 0 1 |  0  2  0  4 |  *  *  * 16

xo4oo ox3oo3oo4oo&#zx   → height = 0
(tegum sum of {4} and perp hex)
(tegum product of {4} with hex)

o.4o. o.3o.3o.4o.    | 4 *  2  8  0 | 16 24  0 | 48  32  0 |  64 16 | 32
.o4.o .o3.o3.o4.o    | * 8  0  4  6 |  4 24 12 | 24  48  8 |  48 32 | 32
---------------------+-----+---------+----------+-----------+--------+---
x. .. .. .. .. ..    | 2 0 | 4  *  *   8  0  0 | 24   0  0 |  32  0 | 16
oo4oo oo3oo3oo4oo&#x | 1 1 | * 32  *   2  6  0 | 12  12  0 |  24  8 | 16
.. .. .x .. .. ..    | 0 2 | *  * 24   0  4  4 |  4  16  4 |  16 16 | 16
---------------------+-----+---------+----------+-----------+--------+---
xo .. .. .. .. ..&#x | 2 1 | 1  2  0 | 32  *  *   6   0  0 |  12  0 |  8
.. .. ox .. .. ..&#x | 1 2 | 0  2  1 |  * 96  *   2   4  0 |   8  4 |  8
.. .. .x3.o .. ..    | 0 3 | 0  0  3 |  *  * 32   0   4  2 |   4  8 |  8
---------------------+-----+---------+----------+-----------+--------+---
xo .. ox .. .. ..&#x  2 2 | 1  4  1 |  2  2  0 | 96   *  * |   4  0 |  4
.. .. ox3oo .. ..&#x  1 3 | 0  3  3 |  0  3  1 |  * 128  * |   2  2 |  4
.. .. .x3.o3.o ..     0 4 | 0  0  6 |  0  0  4 |  *   * 16 |   0  4 |  4
---------------------+-----+---------+----------+-----------+--------+---
xo .. ox3oo .. ..&#x  2 3 | 1  6  3 |  3  6  1 |  3   2  0 | 128  * |  2
.. .. ox3oo3oo ..&#x  1 4 | 0  4  6 |  0  6  4 |  0   4  1 |   * 64 |  2
---------------------+-----+---------+----------+-----------+--------+---
xo .. ox3oo3oo ..&#x  2 4 | 1  8  6 |  4 12  4 |  6   8  1 |   4  2 | 64

xo xo ox3oo3oo *d3oo&#zx   → height = 0
(tegum sum of {4} and perp hex)
(tegum product of {4} with hex)

o. o. o.3o.3o. *d3o.    | 4 *  1 1  8  0 |  8  8 24  0 | 24 24  32 0 0 | 32 32  8  8 |  8  8  8  8
.o .o .o3.o3.o *d3.o    | * 8  0 0  4  6 |  2  2 24 12 | 12 12  48 4 4 | 24 24 16 16 |  8  8  8  8
------------------------+-----+-----------+-------------+---------------+-------------+------------
x. .. .. .. ..    ..    | 2 0 | 2 *  *  *   8  0  0  0 | 24  0   0 0 0 | 32  0  0  0 |  8  8  0  0
.. x. .. .. ..    ..    | 2 0 | * 2  *  *   0  8  0  0 |  0 24   0 0 0 |  0 32  0  0 |  0  0  8  8
oo oo oo3oo3oo *d3oo&#x | 1 1 | * * 32  *   1  1  4  0 |  6  6  12 0 0 | 12 12  4  4 |  4  4  4  4
.. .. .x .. ..    ..    | 0 2 | * *  * 24   0  0  4  2 |  2  2  16 2 2 |  8  8  8  8 |  4  4  4  4
------------------------+-----+-----------+-------------+---------------+-------------+------------
xo .. .. .. ..    ..&#x | 2 1 | 1 0  2  0 | 16  *  *  *   6  0   0 0 0 | 12  0  0  0 |  4  4  0  0
.. xo .. .. ..    ..&#x | 2 1 | 0 1  2  0 |  * 16  *  *   0  6   0 0 0 |  0 12  0  0 |  0  0  4  4
.. .. ox .. ..    ..&#x | 1 2 | 0 0  2  1 |  *  * 96  *   1  1   4 0 0 |  4  4  2  2 |  2  2  2  2
.. .. .x3.o ..    ..    | 0 3 | 0 0  0  3 |  *  *  * 32   0  0   4 1 1 |  2  2  4  4 |  2  2  2  2
------------------------+-----+-----------+-------------+---------------+-------------+------------
xo .. ox .. ..    ..&#x  2 2 | 1 0  4  1 |  2  0  2  0 | 48  *   * * * |  4  0  0  0 |  2  2  0  0
.. xo ox .. ..    ..&#x  2 2 | 0 1  4  1 |  0  2  2  0 |  * 48   * * * |  0  4  0  0 |  0  0  2  2
.. .. ox3oo ..    ..&#x  1 3 | 0 0  3  3 |  0  0  3  1 |  *  * 128 * * |  1  1  1  1 |  1  1  1  1
.. .. .x3.o3.o    ..     0 4 | 0 0  0  6 |  0  0  0  4 |  *  *   * 8 * |  0  0  4  0 |  2  0  2  0
.. .. .x3.o .. *d3.o     0 4 | 0 0  0  6 |  0  0  0  4 |  *  *   * * 8 |  0  0  0  4 |  0  2  0  2
------------------------+-----+-----------+-------------+---------------+-------------+------------
xo .. ox3oo ..    ..&#x  2 3 | 1 0  6  3 |  3  0  6  1 |  3  0   2 0 0 | 64  *  *  * |  1  1  0  0
.. xo ox3oo ..    ..&#x  2 3 | 0 1  6  3 |  0  3  6  1 |  0  3   2 0 0 |  * 64  *  * |  0  0  1  1
.. .. ox3oo3oo    ..&#x  1 4 | 0 0  4  6 |  0  0  6  4 |  0  0   4 1 0 |  *  * 32  * |  1  0  1  0
.. .. ox3oo .. *d3oo&#x  1 4 | 0 0  4  6 |  0  0  6  4 |  0  0   4 0 1 |  *  *  * 32 |  0  1  0  1
------------------------+-----+-----------+-------------+---------------+-------------+------------
xo .. ox3oo3oo    ..&#x  2 4 | 1 0  8  6 |  4  0 12  4 |  6  0   8 1 0 |  4  0  2  0 | 16  *  *  *
xo .. ox3oo .. *d3oo&#x  2 4 | 1 0  8  6 |  4  0 12  4 |  6  0   8 0 1 |  4  0  0  2 |  * 16  *  *
.. xo ox3oo3oo    ..&#x  2 4 | 0 1  8  6 |  0  4 12  4 |  0  6   8 1 0 |  0  4  2  0 |  *  * 16  *
.. xo ox3oo .. *d3oo&#x  2 4 | 0 1  8  6 |  0  4 12  4 |  0  6   8 0 1 |  0  4  0  2 |  *  *  * 16

oxo4ooo xoo3ooo3oox&#xt   → both heights = 1/sqrt(8) = 0.353553
(tet || perp pseudo {4} || dual tet)

o.. o.. o..3o..3o..    | 4 * *  3  4  3 0  0 0 | 3  4 12  6  3 12  0  0 0 | 1 12 12 24 12 3 3 1 12  0  0 0 | 24 12 12 12 4 12  4  0 0 | 12 4 12  4 0
.o. .o. .o.3.o.3.o.    | * 4 *  0  4  0 2  4 0 | 0  8  6  0  0 12  8  6 0 | 0 24 12 12  4 0 0 0 12 12  4 0 | 24  8 24  4 1  6  4  8 1 |  8 2 12  8 2
..o ..o ..o3..o3..o    | * * 4  0  0  3 0  4 3 | 0  0  0  3  6 12  4 12 3 | 0 12  0 12  0 1 3 3 24 12 12 1 | 12  0 24  4 0 12 12 12 4 |  4 0 12 12 4
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
... ... x.. ... ...    | 2 0 0 | 6  *  * *  * *  2  0  4  2  0  0  0  0 0 | 1  0  4  8  8 2 1 0  0  0  0 0 |  8  8  0  8 4  4  0  0 0 |  8 4  4  0 0
oo. oo. oo.3oo.3oo.&#x | 1 1 0 | * 16  * *  * *  0  2  3  0  0  3  0  0 0 | 0  6  6  6  3 0 0 0  3  0  0 0 | 12  6  6  3 1  3  1  0 0 |  6 2  6  2 0
o.o o.o o.o3o.o3o.o&#x | 1 0 1 | *  * 12 *  * *  0  0  0  2  2  4  0  0 0 | 0  4  0  8  0 1 2 1  8  0  0 0 |  8  0  8  4 0  4  4  0 0 |  4 0  8  4 0
.x. ... ... ... ...    | 0 2 0 | *  *  * 4  * *  0  4  0  0  0  0  4  0 0 | 0 12  6  0  0 0 0 0  0  6  0 0 | 12  4 12  0 0  0  0  4 0 |  4 1  6  4 1
.oo .oo .oo3.oo3.oo&#x | 0 1 1 | *  *  * * 16 *  0  0  0  0  0  3  2  3 0 | 0  6  0  3  0 0 0 0  6  6  3 0 |  6  0 12  1 0  3  3  6 1 |  2 0  6  6 2
... ... ... ... ..x    | 0 0 2 | *  *  * *  * 6  0  0  0  0  2  0  0  4 2 | 0  0  0  0  0 0 1 2  8  4  8 1 |  0  0  8  0 0  4  8  8 4 |  0 0  4  8 4
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
... ... x..3o.. ...    | 3 0 0 | 3  0  0 0  0 0 | 4  *  *  *  *  *  *  * *  1  0  0  0  4 1 0 0  0  0  0 0 |  0  4  0  4 4  0  0  0 0 |  4 4  0  0 0
ox. ... ... ... ...&#x | 1 2 0 | 0  2  0 1  0 0 | * 16  *  *  *  *  *  * *  0  3  3  0  0 0 0 0  0  0  0 0 |  6  3  3  0 0  0  0  0 0 |  3 1  3  1 0
... ... xo. ... ...&#x | 2 1 0 | 1  2  0 0  0 0 | *  * 24  *  *  *  *  * *  0  0  2  2  2 0 0 0  0  0  0 0 |  4  4  0  2 1  1  0  0 0 |  4 2  2  0 0
... ... x.o ... ...&#x | 2 0 1 | 1  0  2 0  0 0 | *  *  * 12  *  *  *  * *  0  0  0  4  0 1 1 0  0  0  0 0 |  4  0  0  4 0  4  0  0 0 |  4 0  4  0 0
... ... ... ... o.x&#x | 1 0 2 | 0  0  2 0  0 1 | *  *  *  * 12  *  *  * *  0  0  0  0  0 0 1 1  4  0  0 0 |  0  0  4  0 0  4  4  0 0 |  0 0  4  4 0
ooo ooo ooo3ooo3ooo&#x | 1 1 1 | 0  1  1 0  1 0 | *  *  *  *  * 48  *  * *  0  2  0  2  0 0 0 0  2  0  0 0 |  4  0  4  1 0  2  1  0 0 |  2 0  4  2 0
.xo ... ... ... ...&#x | 0 2 1 | 0  0  0 1  2 0 | *  *  *  *  *  * 16  * *  0  3  0  0  0 0 0 0  0  3  0 0 |  3  0  6  0 0  0  0  3 0 |  1 0  3  3 1
... ... ... ... .ox&#x | 0 1 2 | 0  0  0 0  2 1 | *  *  *  *  *  *  * 24 *  0  0  0  0  0 0 0 0  2  2  2 0 |  0  0  4  0 0  1  4  4 1 |  0 0  2  4 2
... ... ... ..o3..x    | 0 0 3 | 0  0  0 0  0 3 | *  *  *  *  *  *  *  * 4  0  0  0  0  0 0 0 1  0  0  4 1 |  0  0  0  0 0  0  4  4 4 |  0 0  0  4 4
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
... ... x..3o..3o..     4 0 0 | 6  0  0 0  0 0 | 4  0  0  0  0  0  0  0 0 | 1  *  *  *  * * * *  *  *  * * |  0  0  0  0 4  0  0  0 0 |  0 4  0  0 0
oxo ... ... ... ...&#x  1 2 1 | 0  2  1 1  2 0 | 0  1  0  0  0  2  1  0 0 | * 48  *  *  * * * *  *  *  * * |  2  0  2  0 0  0  0  0 0 |  1 0  2  1 0
ox. ... xo. ... ...&#x  2 2 0 | 1  4  0 1  0 0 | 0  2  2  0  0  0  0  0 0 | *  * 24  *  * * * *  *  *  * * |  2  2  0  0 0  0  0  0 0 |  2 1  1  0 0
... ... xoo ... ...&#x  2 1 1 | 1  2  2 0  1 0 | 0  0  1  1  0  2  0  0 0 | *  *  * 48  * * * *  *  *  * * |  2  0  0  1 0  1  0  0 0 |  2 0  2  0 0
... ... xo.3oo. ...&#x  3 1 0 | 3  3  0 0  0 0 | 1  0  3  0  0  0  0  0 0 | *  *  *  * 16 * * *  *  *  * * |  0  2  0  1 1  0  0  0 0 |  2 2  0  0 0
... ... x.o3o.o ...&#x  3 0 1 | 3  0  3 0  0 0 | 1  0  0  3  0  0  0  0 0 | *  *  *  *  * 4 * *  *  *  * * |  0  0  0  4 0  0  0  0 0 |  4 0  0  0 0
... ... x.o ... o.x&#x  2 0 2 | 1  0  4 0  0 1 | 0  0  0  2  2  0  0  0 0 | *  *  *  *  * * 6 *  *  *  * * |  0  0  0  0 0  4  0  0 0 |  0 0  4  0 0
... ... ... o.o3o.x&#x  1 0 3 | 0  0  3 0  0 3 | 0  0  0  0  3  0  0  0 1 | *  *  *  *  * * * 4  *  *  * * |  0  0  0  0 0  0  4  0 0 |  0 0  0  4 0
... ... ... ... oox&#x  1 1 2 | 0  1  2 0  2 1 | 0  0  0  0  1  2  0  1 0 | *  *  *  *  * * * * 48  *  * * |  0  0  2  0 0  1  1  0 0 |  0 0  2  2 0
.xo ... ... ... .ox&#x  0 2 2 | 0  0  0 1  4 1 | 0  0  0  0  0  0  2  2 0 | *  *  *  *  * * * *  * 24  * * |  0  0  2  0 0  0  0  2 0 |  0 0  1  2 1
... ... ... .oo3.ox&#x  0 1 3 | 0  0  0 0  3 3 | 0  0  0  0  0  0  0  3 1 | *  *  *  *  * * * *  *  * 16 * |  0  0  0  2 0  0  1  2 1 |  0 0  0  2 2
... ... ..o3..o3..x     0 0 4 | 0  0  0 0  0 6 | 0  0  0  0  0  0  0  0 4 | *  *  *  *  * * * *  *  *  * 1 |  0  0  0  2 0  0  0  0 4 |  0 0  0  0 4
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
oxo ... xoo ... ...&#x  2 2 1 | 1  4  2 1  2 0 | 0  2  2  1  0  4  1  0 0 | 0  2  1  2  0 0 0 0  0  0  0 0 | 48  *  *  * *  *  *  * * |  1 0  1  0 0
ox. ... xo.3oo. ...&#x  3 2 0 | 3  6  0 1  0 0 | 1  3  6  0  0  0  0  0 0 | 0  0  3  0  2 0 0 0  0  0  0 0 |  * 16  *  * *  *  *  * * |  1 1  0  0 0
oxo ... ... ... oox&#x  1 2 2 | 0  2  2 1  4 1 | 0  1  0  0  1  4  2  2 0 | 0  2  0  0  0 0 0 0  2  1  0 0 |  *  * 48  * *  *  *  * * |  0 0  1  1 0
... ... xoo3ooo ...&#x  3 1 1 | 3  3  3 0  1 0 | 1  0  3  3  0  3  0  0 0 | 0  0  0  3  1 1 0 0  0  0  0 0 |  *  *  * 16 *  *  *  * * |  2 0  0  0 0
... ... xo.3oo.3oo.&#x  4 1 0 | 6  4  0 0  0 0 | 4  0  6  0  0  0  0  0 0 | 1  0  0  0  4 0 0 0  0  0  0 0 |  *  *  *  * 4  *  *  * * |  0 2  0  0 0
... ... xoo ... oox&#x  2 1 2 | 1  2  4 0  2 1 | 0  0  1  2  2  4  0  1 0 | 0  0  0  2  0 0 1 0  2  0  0 0 |  *  *  *  * * 24  *  * * |  0 0  2  0 0
... ... ... ooo3oox&#x  1 1 3 | 0  1  3 0  3 3 | 0  0  0  0  3  3  0  3 1 | 0  0  0  0  0 0 0 1  3  0  1 0 |  *  *  *  * *  * 16  * * |  0 0  0  2 0
.xo ... ... .oo3.ox&#x  0 2 3 | 0  0  0 1  6 3 | 0  0  0  0  0  0  3  6 1 | 0  0  0  0  0 0 0 0  0  3  2 0 |  *  *  *  * *  *  * 16 * |  0 0  0  1 1
... ... .oo3.oo3.ox&#x  0 1 4 | 0  0  0 0  4 6 | 0  0  0  0  0  0  0  6 4 | 0  0  0  0  0 0 0 0  0  0  4 1 |  *  *  *  * *  *  *  * 4 |  0 0  0  0 2
-----------------------+-------+----------------+--------------------------+--------------------------------+--------------------------+-------------
oxo ... xoo3ooo ...&#x  3 2 1 | 3  6  3 1  2 0 | 1  3  6  3  0  6  1  0 0 | 0  3  3  6  2 1 0 0  0  0  0 0 |  3  1  0  2 0  0  0  0 0 | 16 *  *  * *
ox. ... xo.3oo.3oo.&#x  4 2 0 | 6  8  0 1  0 0 | 4  4 12  0  0  0  0  0 0 | 1  0  6  0  8 0 0 0  0  0  0 0 |  0  4  0  0 2  0  0  0 0 |  * 4  *  * *
oxo ... xoo ... oox&#x  2 2 2 | 1  4  4 1  4 1 | 0  2  2  2  2  8  2  2 0 | 0  4  1  4  0 0 1 0  4  1  0 0 |  2  0  2  0 0  2  0  0 0 |  * * 24  * *
oxo ... ... ooo3oox&#x  1 2 3 | 0  2  3 1  6 3 | 0  1  0  0  3  6  3  6 1 | 0  3  0  0  0 0 0 1  6  3  2 0 |  0  0  3  0 0  0  2  1 0 |  * *  * 16 *
.xo ... .oo3.oo3.ox&#x  0 2 4 | 0  0  0 1  8 6 | 0  0  0  0  0  0  4 12 4 | 0  0  0  0  0 0 0 0  0  6  8 1 |  0  0  0  0 0  0  0  4 2 |  * *  *  * 4

oxo oxo xoo3ooo3oox&#xt   → both heights = 1/sqrt(8) = 0.353553
(tet || perp pseudo {4} || dual tet)

o.. o.. o..3o..3o..    | 4 * *  3  4  3 0 0  0 0 | 3 2 2 12  6  3 12 0 0  0 0 | 1  6  6  6  6 24 12 3 3 1 12  0  0  0 0 | 12 6  6 12 6  6 12 4 12  4 0 0 0 | 6 2  6 2 6 2  6 2 0 0
.o. .o. .o.3.o.3.o.    | * 4 *  0  4  0 1 1  4 0 | 0 4 4  6  0  0 12 4 4  6 0 | 0 12  6 12  6 12  4 0 0 0 12  6  6  4 0 | 12 4 12 12 4 12  4 1  6  4 4 4 1 | 4 1  6 4 4 1  6 4 1 1
..o ..o ..o3..o3..o    | * * 4  0  0  3 0 0  4 3 | 0 0 0  0  3  6 12 2 2 12 3 | 0  6  0  6  0 12  0 1 3 3 24  6  6 12 1 |  6 0 12  6 0 12  4 0 12 12 6 6 4 | 2 0  6 6 2 0  6 6 2 2
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
... ... x.. ... ...    | 2 0 0 | 6  *  * * *  * *  2 0 0  4  2  0  0 0 0  0 0 | 1  0  2  0  2  8  8 2 1 0  0  0  0  0 0 |  4 4  0  4 4  0  8 4  4  0 0 0 0 | 4 2  2 0 4 2  2 0 0 0
oo. oo. oo.3oo.3oo.&#x | 1 1 0 | * 16  * * *  * *  0 1 1  3  0  0  3 0 0  0 0 | 0  3  3  3  3  6  3 0 0 0  3  0  0  0 0 |  6 3  3  6 3  3  3 1  3  1 0 0 0 | 3 1  3 1 3 1  3 1 0 0
o.o o.o o.o3o.o3o.o&#x | 1 0 1 | *  * 12 * *  * *  0 0 0  0  2  2  4 0 0  0 0 | 0  2  0  2  0  8  0 1 2 1  8  0  0  0 0 |  4 0  4  4 0  4  4 0  4  4 0 0 0 | 2 0  4 2 2 0  4 2 0 0
.x. ... ... ... ...    | 0 2 0 | *  *  * 2 *  * *  0 4 0  0  0  0  0 4 0  0 0 | 0 12  6  0  0  0  0 0 0 0  0  6  0  0 0 | 12 4 12  0 0  0  0 0  0  0 4 0 0 | 4 1  6 4 0 0  0 0 1 0
... .x. ... ... ...    | 0 2 0 | *  *  * * 2  * *  0 0 4  0  0  0  0 0 4  0 0 | 0  0  0 12  6  0  0 0 0 0  0  0  6  0 0 |  0 0  0 12 4 12  0 0  0  0 0 4 0 | 0 0  0 0 4 1  6 4 0 1
.oo .oo .oo3.oo3.oo&#x | 0 1 1 | *  *  * * * 16 *  0 0 0  0  0  0  3 1 1  3 0 | 0  3  0  3  0  3  0 0 0 0  6  3  3  3 0 |  3 0  6  3 0  6  1 0  3  3 3 3 1 | 1 0  3 3 1 0  3 3 1 1
... ... ... ... ..x    | 0 0 2 | *  *  * * *  * 6  0 0 0  0  0  2  0 0 0  4 2 | 0  0  0  0  0  0  0 0 1 2  8  2  2  8 1 |  0 0  4  0 0  4  0 0  4  8 4 4 4 | 0 0  2 4 0 0  2 4 2 2
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
... ... x..3o.. ...    | 3 0 0 | 3  0  0 0 0  0 0 | 4 * *  *  *  *  * * *  * *  1  0  0  0  0  0  4 1 0 0  0  0  0  0 0 |  0 2  0  0 2  0  4 4  0  0 0 0 0 | 2 2  0 0 2 2  0 0 0 0
ox. ... ... ... ...&#x | 1 2 0 | 0  2  0 1 0  0 0 | * 8 *  *  *  *  * * *  * *  0  3  3  0  0  0  0 0 0 0  0  0  0  0 0 |  6 3  3  0 0  0  0 0  0  0 0 0 0 | 3 1  3 1 0 0  0 0 0 0
... ox. ... ... ...&#x | 1 2 0 | 0  2  0 0 1  0 0 | * * 8  *  *  *  * * *  * *  0  0  0  3  3  0  0 0 0 0  0  0  0  0 0 |  0 0  0  6 3  3  0 0  0  0 0 0 0 | 0 0  0 0 3 1  3 1 0 0
... ... xo. ... ...&#x | 2 1 0 | 1  2  0 0 0  0 0 | * * * 24  *  *  * * *  * *  0  0  1  0  1  2  2 0 0 0  0  0  0  0 0 |  2 2  0  2 2  0  2 1  1  0 0 0 0 | 2 1  1 0 2 1  1 0 0 0
... ... x.o ... ...&#x | 2 0 1 | 1  0  2 0 0  0 0 | * * *  * 12  *  * * *  * *  0  0  0  0  0  4  0 1 1 0  0  0  0  0 0 |  2 0  0  2 0  0  4 0  4  0 0 0 0 | 2 0  2 0 2 0  2 0 0 0
... ... ... ... o.x&#x | 1 0 2 | 0  0  2 0 0  0 1 | * * *  *  * 12  * * *  * *  0  0  0  0  0  0  0 0 1 1  4  0  0  0 0 |  0 0  2  0 0  2  0 0  4  4 0 0 0 | 0 0  2 2 0 0  2 2 0 0
ooo ooo ooo3ooo3ooo&#x | 1 1 1 | 0  1  1 0 0  1 0 | * * *  *  *  * 48 * *  * *  0  1  0  1  0  2  0 0 0 0  2  0  0  0 0 |  2 0  2  2 0  2  1 0  2  1 0 0 0 | 1 0  2 1 1 0  2 1 0 0
.xo ... ... ... ...&#x | 0 2 1 | 0  0  0 1 0  2 0 | * * *  *  *  *  * 8 *  * *  0  3  0  0  0  0  0 0 0 0  0  3  0  0 0 |  3 0  6  0 0  0  0 0  0  0 3 0 0 | 1 0  3 3 0 0  0 0 1 0
... .xo ... ... ...&#x | 0 2 1 | 0  0  0 0 1  2 0 | * * *  *  *  *  * * 8  * *  0  0  0  3  0  0  0 0 0 0  0  0  3  0 0 |  0 0  0  3 0  6  0 0  0  0 0 3 0 | 0 0  0 0 1 0  3 3 0 1
... ... ... ... .ox&#x | 0 1 2 | 0  0  0 0 0  2 1 | * * *  *  *  *  * * * 24 *  0  0  0  0  0  0  0 0 0 0  2  1  1  2 0 |  0 0  2  0 0  2  0 0  1  4 2 2 1 | 0 0  1 2 0 0  1 2 1 1
... ... ... ..o3..x    | 0 0 3 | 0  0  0 0 0  0 3 | * * *  *  *  *  * * *  * 4  0  0  0  0  0  0  0 0 0 1  0  0  0  4 1 |  0 0  0  0 0  0  0 0  0  4 2 2 4 | 0 0  0 2 0 0  0 2 2 2
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
... ... x..3o..3o..     4 0 0 | 6  0  0 0 0  0 0 | 4 0 0  0  0  0  0 0 0  0 0 | 1  *  *  *  *  *  * * * *  *  *  *  * * |  0 0  0  0 0  0  0 4  0  0 0 0 0 | 0 2  0 0 0 2  0 0 0 0
oxo ... ... ... ...&#x  1 2 1 | 0  2  1 1 0  2 0 | 0 1 0  0  0  0  2 1 0  0 0 | * 24  *  *  *  *  * * * *  *  *  *  * * |  2 0  2  0 0  0  0 0  0  0 0 0 0 | 1 0  2 1 0 0  0 0 0 0
ox. ... xo. ... ...&#x  2 2 0 | 1  4  0 1 0  0 0 | 0 2 0  2  0  0  0 0 0  0 0 | *  * 12  *  *  *  * * * *  *  *  *  * * |  2 2  0  0 0  0  0 0  0  0 0 0 0 | 2 1  1 0 0 0  0 0 0 0
... oxo ... ... ...&#x  1 2 1 | 0  2  1 0 1  2 0 | 0 0 1  0  0  0  2 0 1  0 0 | *  *  * 24  *  *  * * * *  *  *  *  * * |  0 0  0  2 0  2  0 0  0  0 0 0 0 | 0 0  0 0 1 0  2 1 0 0
... ox. xo. ... ...&#x  2 2 0 | 1  4  0 0 1  0 0 | 0 0 2  2  0  0  0 0 0  0 0 | *  *  *  * 12  *  * * * *  *  *  *  * * |  0 0  0  2 2  0  0 0  0  0 0 0 0 | 0 0  0 0 2 1  1 0 0 0
... ... xoo ... ...&#x  2 1 1 | 1  2  2 0 0  1 0 | 0 0 0  1  1  0  2 0 0  0 0 | *  *  *  *  * 48  * * * *  *  *  *  * * |  1 0  0  1 0  0  1 0  1  0 0 0 0 | 1 0  1 0 1 0  1 0 0 0
... ... xo.3oo. ...&#x  3 1 0 | 3  3  0 0 0  0 0 | 1 0 0  3  0  0  0 0 0  0 0 | *  *  *  *  *  * 16 * * *  *  *  *  * * |  0 1  0  0 1  0  1 1  0  0 0 0 0 | 1 1  0 0 1 1  0 0 0 0
... ... x.o3o.o ...&#x  3 0 1 | 3  0  3 0 0  0 0 | 1 0 0  0  3  0  0 0 0  0 0 | *  *  *  *  *  *  * 4 * *  *  *  *  * * |  0 0  0  0 0  0  4 0  0  0 0 0 0 | 2 0  0 0 2 0  0 0 0 0
... ... x.o ... o.x&#x  2 0 2 | 1  0  4 0 0  0 1 | 0 0 0  0  2  2  0 0 0  0 0 | *  *  *  *  *  *  * * 6 *  *  *  *  * * |  0 0  0  0 0  0  0 0  4  0 0 0 0 | 0 0  2 0 0 0  2 0 0 0
... ... ... o.o3o.x&#x  1 0 3 | 0  0  3 0 0  0 3 | 0 0 0  0  0  3  0 0 0  0 1 | *  *  *  *  *  *  * * * 4  *  *  *  * * |  0 0  0  0 0  0  0 0  0  4 0 0 0 | 0 0  0 2 0 0  0 2 0 0
... ... ... ... oox&#x  1 1 2 | 0  1  2 0 0  2 1 | 0 0 0  0  0  1  2 0 0  1 0 | *  *  *  *  *  *  * * * * 48  *  *  * * |  0 0  1  0 0  1  0 0  1  1 0 0 0 | 0 0  1 1 0 0  1 1 0 0
.xo ... ... ... .ox&#x  0 2 2 | 0  0  0 1 0  4 1 | 0 0 0  0  0  0  0 2 0  2 0 | *  *  *  *  *  *  * * * *  * 12  *  * * |  0 0  2  0 0  0  0 0  0  0 2 0 0 | 0 0  1 2 0 0  0 0 1 0
... .xo ... ... .ox&#x  0 2 2 | 0  0  0 0 1  4 1 | 0 0 0  0  0  0  0 0 2  2 0 | *  *  *  *  *  *  * * * *  *  * 12  * * |  0 0  0  0 0  2  0 0  0  0 0 2 0 | 0 0  0 0 0 0  1 2 0 1
... ... ... .oo3.ox&#x  0 1 3 | 0  0  0 0 0  3 3 | 0 0 0  0  0  0  0 0 0  3 1 | *  *  *  *  *  *  * * * *  *  *  * 16 * |  0 0  0  0 0  0  2 0  0  1 1 1 1 | 0 0  0 1 0 0  0 1 1 1
... ... ..o3..o3..x     0 0 4 | 0  0  0 0 0  0 6 | 0 0 0  0  0  0  0 0 0  0 4 | *  *  *  *  *  *  * * * *  *  *  *  * 1 |  0 0  0  0 0  0  2 0  0  0 0 0 4 | 0 0  0 0 0 0  0 0 2 2
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
oxo ... xoo ... ...&#x  2 2 1 | 1  4  2 1 0  2 0 | 0 2 0  2  1  0  4 1 0  0 0 | 0  2  1  0  0  2  0 0 0 0  0  0  0  0 0 | 24 *  *  * *  *  * *  *  * * * * | 1 0  1 0 0 0  0 0 0 0
ox. ... xo.3oo. ...&#x  3 2 0 | 3  6  0 1 0  0 0 | 1 3 0  6  0  0  0 0 0  0 0 | 0  0  3  0  0  0  2 0 0 0  0  0  0  0 0 |  * 8  *  * *  *  * *  *  * * * * | 1 1  0 0 0 0  0 0 0 0
oxo ... ... ... oox&#x  1 2 2 | 0  2  2 1 0  4 1 | 0 1 0  0  0  1  4 2 0  2 0 | 0  2  0  0  0  0  0 0 0 0  2  1  0  0 0 |  * * 24  * *  *  * *  *  * * * * | 0 0  1 1 0 0  0 0 0 0
... oxo xoo ... ...&#x  2 2 1 | 1  4  2 0 1  2 0 | 0 0 2  2  1  0  4 0 1  0 0 | 0  0  0  2  1  2  0 0 0 0  0  0  0  0 0 |  * *  * 24 *  *  * *  *  * * * * | 0 0  0 0 1 0  1 0 0 0
... ox. xo.3oo. ...&#x  3 2 0 | 3  6  0 0 1  0 0 | 1 0 3  6  0  0  0 0 0  0 0 | 0  0  0  0  3  0  2 0 0 0  0  0  0  0 0 |  * *  *  * 8  *  * *  *  * * * * | 0 0  0 0 1 1  0 0 0 0
... oxo ... ... oox&#x  1 2 2 | 0  2  2 0 1  4 1 | 0 0 1  0  0  1  4 0 2  2 0 | 0  0  0  2  0  0  0 0 0 0  2  0  1  0 0 |  * *  *  * * 24  * *  *  * * * * | 0 0  0 0 0 0  1 1 0 0
... ... xoo3ooo ...&#x  3 1 1 | 3  3  3 0 0  1 0 | 1 0 0  3  3  0  3 0 0  0 0 | 0  0  0  0  0  3  1 1 0 0  0  0  0  0 0 |  * *  *  * *  * 16 *  *  * * * * | 1 0  0 0 1 0  0 0 0 0
... ... xo.3oo.3oo.&#x  4 1 0 | 6  4  0 0 0  0 0 | 4 0 0  6  0  0  0 0 0  0 0 | 1  0  0  0  0  0  4 0 0 0  0  0  0  0 0 |  * *  *  * *  *  * 4  *  * * * * | 0 1  0 0 0 1  0 0 0 0
... ... xoo ... oox&#x  2 1 2 | 1  2  4 0 0  2 1 | 0 0 0  1  2  2  4 0 0  1 0 | 0  0  0  0  0  2  0 0 1 0  2  0  0  0 0 |  * *  *  * *  *  * * 24  * * * * | 0 0  1 0 0 0  1 0 0 0
... ... ... ooo3oox&#x  1 1 3 | 0  1  3 0 0  3 3 | 0 0 0  0  0  3  3 0 0  3 1 | 0  0  0  0  0  0  0 0 0 1  3  0  0  1 0 |  * *  *  * *  *  * *  * 16 * * * | 0 0  0 1 0 0  0 1 0 0
.xo ... ... .oo3.ox&#x  0 2 3 | 0  0  0 1 0  6 3 | 0 0 0  0  0  0  0 3 0  6 1 | 0  0  0  0  0  0  0 0 0 0  0  3  0  2 0 |  * *  *  * *  *  * *  *  * 8 * * | 0 0  0 1 0 0  0 0 1 0
... .xo ... .oo3.ox&#x  0 2 3 | 0  0  0 0 1  6 3 | 0 0 0  0  0  0  0 0 3  6 1 | 0  0  0  0  0  0  0 0 0 0  0  0  3  2 0 |  * *  *  * *  *  * *  *  * * 8 * | 0 0  0 0 0 0  0 1 0 1
... ... .oo3.oo3.ox&#x  0 1 4 | 0  0  0 0 0  4 6 | 0 0 0  0  0  0  0 0 0  6 4 | 0  0  0  0  0  0  0 0 0 0  0  0  0  4 1 |  * *  *  * *  *  * *  *  * * * 4 | 0 0  0 0 0 0  0 0 1 1
-----------------------+-------+------------------+----------------------------+-----------------------------------------+----------------------------------+----------------------
oxo ... xoo3ooo ...&#x  3 2 1 | 3  6  3 1 0  2 0 | 1 3 0  6  3  0  6 1 0  0 0 | 0  3  3  0  0  6  2 1 0 0  0  0  0  0 0 |  3 1  0  0 0  0  2 0  0  0 0 0 0 | 8 *  * * * *  * * * *
ox. ... xo.3oo.3oo.&#x  4 2 0 | 6  8  0 1 0  0 0 | 4 4 0 12  0  0  0 0 0  0 0 | 1  0  6  0  0  0  8 0 0 0  0  0  0  0 0 |  0 4  0  0 0  0  0 2  0  0 0 0 0 | * 2  * * * *  * * * *
oxo ... xoo ... oox&#x  2 2 2 | 1  4  4 1 0  4 1 | 0 2 0  2  2  2  8 2 0  2 0 | 0  4  1  0  0  4  0 0 1 0  4  1  0  0 0 |  2 0  2  0 0  0  0 0  2  0 0 0 0 | * * 12 * * *  * * * *
oxo ... ... ooo3oox&#x  1 2 3 | 0  2  3 1 0  6 3 | 0 1 0  0  0  3  6 3 0  6 1 | 0  3  0  0  0  0  0 0 0 1  6  3  0  2 0 |  0 0  3  0 0  0  0 0  0  2 1 0 0 | * *  * 8 * *  * * * *
... oxo xoo3ooo ...&#x  3 2 1 | 3  6  3 0 1  2 0 | 1 0 3  6  3  0  6 0 1  0 0 | 0  0  0  3  3  6  2 1 0 0  0  0  0  0 0 |  0 0  0  3 1  0  2 0  0  0 0 0 0 | * *  * * 8 *  * * * *
... ox. xo.3oo.3oo.&#x  4 2 0 | 6  8  0 0 1  0 0 | 4 0 4 12  0  0  0 0 0  0 0 | 1  0  0  0  6  0  8 0 0 0  0  0  0  0 0 |  0 0  0  0 4  0  0 2  0  0 0 0 0 | * *  * * * 2  * * * *
... oxo xoo ... oox&#x  2 2 2 | 1  4  4 0 1  4 1 | 0 0 2  2  2  2  8 0 2  2 0 | 0  0  0  4  1  4  0 0 1 0  4  0  1  0 0 |  0 0  0  2 0  2  0 0  2  0 0 0 0 | * *  * * * * 12 * * *
... oxo ... ooo3oox&#x  1 2 3 | 0  2  3 0 1  6 3 | 0 0 1  0  0  3  6 0 3  6 1 | 0  0  0  3  0  0  0 0 0 1  6  0  3  2 0 |  0 0  0  0 0  3  0 0  0  2 0 1 0 | * *  * * * *  * 8 * *
.xo ... .oo3.oo3.ox&#x  0 2 4 | 0  0  0 1 0  8 6 | 0 0 0  0  0  0  0 4 0 12 4 | 0  0  0  0  0  0  0 0 0 0  0  6  0  8 1 |  0 0  0  0 0  0  0 0  0  0 4 0 2 | * *  * * * *  * * 2 *
... .xo .oo3.oo3.ox&#x  0 2 4 | 0  0  0 0 1  8 6 | 0 0 0  0  0  0  0 0 4 12 4 | 0  0  0  0  0  0  0 0 0 0  0  0  6  8 1 |  0 0  0  0 0  0  0 0  0  0 0 4 2 | * *  * * * *  * * * 2

xoxo oxoo3oooo3ooox&#xr   → height(1,2) = height(1,4) = height(2,3) = height(3,4) = sqrt(5/8) = 0.790569
                            height(1,3) = 1
                            height(2,4) = 1/sqrt(2) = 0.707107

o... o...3o...3o...    & | 4 *  1  8 1  0  0 |  8 12  8 12 0  0 | 12  8 12 12 24 12 0 0 0 |  8 2  8 24  8  6 24 | 2 2  8  6  8  6
.o.. .o..3.o..3.o..    & | * 8  0  4 0  3  3 |  2 12  2 12 3  9 |  6 12  8  8 36  6 1 4 3 |  6 4  6 18 16 12 18 | 2 2  8  6  8  6
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
x... .... .... ....    & | 2 0 | 2  * *  *  *   8  0  0  0 0  0 | 12  0  0 12  0  0 0 0 0 |  8 0  0  8  0  0  0 | 2 0  8  6  0  0
oo.. oo..3oo..3oo..&#x & | 1 1 | * 32 *  *  *   1  3  1  3 0  0 |  3  3  3  3  9  3 0 0 0 |  3 1  3  9  4  3  9 | 1 1  4  3  4  3
o.o. o.o.3o.o.3o.o.&#x   | 2 0 | *  * 2  *  *   0  0  8  0 0  0 |  0  0 12  0  0 12 0 0 0 |  0 0  8  0  0  0 24 | 0 2  0  0  8  6
.... .x.. .... ....    & | 0 2 | *  * * 12  *   0  4  0  0 2  2 |  2  8  2  0  8  0 1 2 1 |  4 4  4  4  8  4  4 | 2 2  4  2  4  2
.o.o .o.o3.o.o3.o.o&#x   | 0 2 | *  * *  * 12   0  0  0  4 0  4 |  0  0  0  2 16  2 0 2 2 |  0 0  0  8  8  8  8 | 0 0  4  4  4  4
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
xo.. .... .... ....&#x & | 2 1 | 1  2 0  0  0 | 16  *  *  * *  *   3  0  0  3  0  0 0 0 0 |  3 0  0  9  0  0  0 | 1 0  4  3  0  0
.... ox.. .... ....&#x & | 1 2 | 0  2 0  1  0 |  * 48  *  * *  *   1  2  1  0  2  0 0 0 0 |  2 1  2  2  2  1  2 | 1 1  2  1  2  1
ooo. ooo.3ooo.3ooo.&#x & | 2 1 | 0  2 1  0  0 |  *  * 16  * *  *   0  0  3  0  0  3 0 0 0 |  0 0  3  0  0  0  9 | 0 1  0  0  4  3
oo.o oo.o3oo.o3oo.o&#x & | 1 2 | 0  2 0  0  1 |  *  *  * 48 *  *   0  0  0  1  4  1 0 0 0 |  0 0  0  4  2  2  4 | 0 0  2  2  2  2
.... .x..3.o.. ....    & | 0 3 | 0  0 0  3  0 |  *  *  *  * 8  *   0  4  0  0  0  0 1 1 0 |  2 4  2  0  4  0  0 | 2 2  2  0  2  0
.... .x.o .... ....&#x & | 0 3 | 0  0 0  1  2 |  *  *  *  * * 24   0  0  0  0  4  0 0 1 1 |  0 0  0  2  4  4  2 | 0 0  2  2  2  2
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
xo.. ox.. .... ....&#x &  2 2 | 1  4 0  1  0 |  2  2  0  0 0  0 | 24  *  *  *  *  * * * * |  2 0  0  2  0  0  0 | 1 0  2  1  0  0
.... ox..3oo.. ....&#x &  1 3 | 0  3 0  3  0 |  0  3  0  0 1  0 |  * 32  *  *  *  * * * * |  1 1  1  0  1  0  0 | 1 1  1  0  1  0
.... oxo. .... ....&#x &  2 2 | 0  4 1  1  0 |  0  2  2  0 0  0 |  *  * 24  *  *  * * * * |  0 0  2  0  0  0  2 | 0 1  0  0  2  1
xo.o .... .... ....&#x &  2 2 | 1  4 0  0  1 |  2  0  0  2 0  0 |  *  *  * 24  *  * * * * |  0 0  0  4  0  0  0 | 0 0  2  2  0  0
.... ox.o .... ....&#x &  1 3 | 0  3 0  1  2 |  0  1  0  2 0  1 |  *  *  *  * 96  * * * * |  0 0  0  1  1  1  1 | 0 0  1  1  1  1
oooo oooo3oooo3oooo&#x    2 2 | 0  4 1  0  1 |  0  0  2  2 0  0 |  *  *  *  *  * 24 * * * |  0 0  0  0  0  0  4 | 0 0  0  0  2  2
.... .x..3.o..3.o..    &  0 4 | 0  0 0  6  0 |  0  0  0  0 4  0 |  *  *  *  *  *  * 2 * * |  0 4  0  0  0  0  0 | 2 2  0  0  0  0
.... .x.o3.o.o ....&#x &  0 4 | 0  0 0  3  3 |  0  0  0  0 1  3 |  *  *  *  *  *  * * 8 * |  0 0  0  0  4  0  0 | 0 0  2  0  2  0
.... .x.o .... .o.x&#x    0 4 | 0  0 0  2  4 |  0  0  0  0 0  4 |  *  *  *  *  *  * * * 6 |  0 0  0  0  0  4  0 | 0 0  0  2  0  2
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
xo.. ox..3oo.. ....&#x &  2 3 | 1  6 0  3  0 |  3  6  0  0 1  0 |  3  2  0  0  0  0 0 0 0 | 16 *  *  *  *  *  * | 1 0  1  0  0  0
.... ox..3oo..3oo..&#x &  1 4 | 0  4 0  6  0 |  0  6  0  0 4  0 |  0  4  0  0  0  0 1 0 0 |  * 8  *  *  *  *  * | 1 1  0  0  0  0
.... oxo.3ooo. ....&#x &  2 3 | 0  6 1  3  0 |  0  6  3  0 1  0 |  0  2  3  0  0  0 0 0 0 |  * * 16  *  *  *  * | 0 1  0  0  1  0
xo.o ox.o .... ....&#x &  2 3 | 1  6 0  1  2 |  3  2  0  4 0  1 |  1  0  0  2  2  0 0 0 0 |  * *  * 48  *  *  * | 0 0  1  1  0  0
.... ox.o3oo.o ....&#x &  1 4 | 0  4 0  3  3 |  0  3  0  3 1  3 |  0  1  0  0  3  0 0 1 0 |  * *  *  * 32  *  * | 0 0  1  0  1  0
.... ox.o .... oo.x&#x &  1 4 | 0  4 0  2  4 |  0  2  0  4 0  4 |  0  0  0  0  4  0 0 0 1 |  * *  *  *  * 24  * | 0 0  0  1  0  1
.... oxoo .... ....&#x &  2 3 | 0  6 1  1  2 |  0  2  3  4 0  1 |  0  0  1  0  2  2 0 0 0 |  * *  *  *  *  * 48 | 0 0  0  0  1  1
-------------------------+-----+--------------+------------------+-------------------------+---------------------+----------------
xo.. ox..3oo..3oo..&#x &  2 4 | 1  8 0  6  0 |  4 12  0  0 4  0 |  6  8  0  0  0  0 1 0 0 |  4 2  0  0  0  0  0 | 4 *  *  *  *  *
.... oxo.3ooo.3ooo.&#x &  2 4 | 0  8 1  6  0 |  0 12  4  0 4  0 |  0  8  6  0  0  0 1 0 0 |  0 2  4  0  0  0  0 | * 4  *  *  *  *
xo.o ox.o3oo.o ....&#x &  2 4 | 1  8 0  3  3 |  4  6  0  6 1  3 |  3  2  0  3  6  0 0 1 0 |  1 0  0  3  2  0  0 | * * 16  *  *  *
xo.o ox.o .... oo.x&#x &  2 4 | 1  8 0  2  4 |  4  4  0  8 0  4 |  2  0  0  4  8  0 0 0 1 |  0 0  0  4  0  2  0 | * *  * 12  *  *
.... oxoo3oooo ....&#x &  2 4 | 0  8 1  3  3 |  0  6  4  6 1  3 |  0  2  3  0  6  3 0 1 0 |  0 0  1  0  2  0  3 | * *  *  * 16  *
.... oxoo .... ooox&#x    2 4 | 0  8 1  2  4 |  0  4  4  8 0  4 |  0  0  2  0  8  4 0 0 1 |  0 0  0  0  0  2  4 | * *  *  *  * 12

xoo3oox oxo3ooo4ooo&#xt   → both heights = 1/sqrt(6) = 0.408248
({3} || pseudo perp oct || dual {3})

o..3o.. o..3o..4o..     & | 6 *  2  6 2  0 | 1 12 12 3 12 0 |  6 24  8 18 24 | 12 16 36 16 |  8 24
.o.3.o. .o.3.o.4.o.       | * 6  0  6 0  4 | 0  6 24 0  6 4 |  2 24 24  6 24 |  8 24 24 24 |  8 24
--------------------------+-----+-----------+----------------+----------------+-------------+------
x.. ... ... ... ...     & | 2 0 | 6  * *  *  1  6  0 1  0 0 |  6 12  0  6  0 | 12  8 12  0 |  8  8
oo.3oo. oo.3oo.4oo.&#x  & | 1 1 | * 36 *  *  0  2  4 0  2 0 |  1  8  4  3  8 |  4  8 12  8 |  4 12
o.o3o.o o.o3o.o4o.o&#x    | 2 0 | *  * 6  *  0  0  0 2  6 0 |  0  0  0 12 12 |  0  0 24  8 |  0 16
... ... .x. ... ...       | 0 2 | *  * * 12  0  0  6 0  0 2 |  0  6 12  0  6 |  2 12  6 12 |  4 12
--------------------------+-----+-----------+----------------+----------------+-------------+------
x..3o.. ... ... ...     & | 3 0 | 3  0 0  0 | 2  *  * *  * *   6  0  0  0  0 | 12  0  0  0 |  8  0
xo. ... ... ... ...&#x  & | 2 1 | 1  2 0  0 | * 36  * *  * *   1  4  0  1  0 |  4  4  4  0 |  4  4
... ... ox. ... ...&#x  & | 1 2 | 0  2 0  1 | *  * 72 *  * *   0  2  2  0  2 |  1  4  3  4 |  2  6
x.o ... ... ... ...&#x  & | 3 0 | 1  0 2  0 | *  *  * 6  * *   0  0  0  6  0 |  0  0 12  0 |  0  8
ooo3ooo ooo3ooo4ooo&#x    | 2 1 | 0  2 1  0 | *  *  * * 36 *   0  0  0  2  4 |  0  0  8  4 |  0  8
... ... .x.3.o. ...       | 0 3 | 0  0 0  3 | *  *  * *  * 8   0  0  6  0  0 |  0  6  0  6 |  2  6
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ... ... ...&#x  &  3 1 | 3  3 0  0 | 1  3  0 0  0 0 | 12  *  *  *  * |  4  0  0  0 |  4  0
xo. ... ox. ... ...&#x  &  2 2 | 1  4 0  1 | 0  2  2 0  0 0 |  * 72  *  *  * |  1  2  1  0 |  2  2
... ... ox.3oo. ...&#x  &  1 3 | 0  3 0  3 | 0  0  3 0  0 1 |  *  * 48  *  * |  0  2  0  2 |  1  3
xoo ... ... ... ...&#x  &  3 1 | 1  3 2  0 | 0  1  0 1  2 0 |  *  *  * 36  * |  0  0  4  0 |  0  4
... ... oxo ... ...&#x     2 2 | 0  4 1  1 | 0  0  2 0  2 0 |  *  *  *  * 72 |  0  0  2  2 |  0  4
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ox. ... ...&#x  &  3 2 | 3  6 0  1 | 1  6  3 0  0 0 |  2  3  0  0  0 | 24  *  *  * |  2  0
xo. ... ox.3oo. ...&#x  &  2 3 | 1  6 0  3 | 0  3  6 0  0 1 |  0  3  2  0  0 |  * 48  *  * |  1  1
xoo ... oxo ... ...&#x  &  3 2 | 1  6 2  1 | 0  2  3 1  4 0 |  0  1  0  2  2 |  *  * 72  * |  0  2
... ... oxo3ooo ...&#x     2 3 | 0  6 1  3 | 0  0  6 0  3 1 |  0  0  2  0  3 |  *  *  * 48 |  0  2
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ox.3oo. ...&#x  &  3 3 | 3  9 0  3 | 1  9  9 0  0 1 |  3  9  3  0  0 |  3  3  0  0 | 16  *
xoo ... oxo3ooo ...&#x     3 3 | 1  9 2  3 | 0  3  9 1  6 1 |  0  3  3  3  6 |  0  1  3  2 |  * 48

xoo3oox ooo3oxo3ooo&#xt   → both heights = 1/sqrt(6) = 0.408248
({3} || pseudo perp oct || dual {3})

o..3o.. o..3o..3o..     & | 6 *  2  6 2  0 | 1 12 12 3 12 0 0 |  6 24  4  4 18 24 | 12  8  8 36  8  8 | 4 4 12 12
.o.3.o. .o.3.o.3.o.       | * 6  0  6 0  4 | 0  6 24 0  6 2 2 |  2 24 12 12  6 24 |  8 12 12 24 12 12 | 4 4 12 12
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
x.. ... ... ... ...     & | 2 0 | 6  * *  *  1  6  0 1  0 0 0 |  6 12  0  0  6  0 | 12  4  4 12  0  0 | 4 4  4  4
oo.3oo. oo.3oo.3oo.&#x  & | 1 1 | * 36 *  *  0  2  4 0  2 0 0 |  1  8  2  2  3  8 |  4  4  4 12  4  4 | 2 2  6  6
o.o3o.o o.o3o.o3o.o&#x    | 2 0 | *  * 6  *  0  0  0 2  6 0 0 |  0  0  0  0 12 12 |  0  0  0 24  4  4 | 0 0  8  8
... ... ... .x. ...       | 0 2 | *  * * 12  0  0  6 0  0 1 1 |  0  6  6  6  0  6 |  2  6  6  6  6  6 | 2 2  6  6
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
x..3o.. ... ... ...     & | 3 0 | 3  0 0  0 | 2  *  * *  * * *   6  0  0  0  0  0 | 12  0  0  0  0  0 | 4 4  0  0
xo. ... ... ... ...&#x  & | 2 1 | 1  2 0  0 | * 36  * *  * * *   1  4  0  0  1  0 |  4  2  2  4  0  0 | 2 2  2  2
... ... ... ox. ...&#x  & | 1 2 | 0  2 0  1 | *  * 72 *  * * *   0  2  1  1  0  2 |  1  2  2  3  2  2 | 1 1  3  3
x.o ... ... ... ...&#x  & | 3 0 | 1  0 2  0 | *  *  * 6  * * *   0  0  0  0  6  0 |  0  0  0 12  0  0 | 0 0  4  4
ooo3ooo ooo3ooo3ooo&#x    | 2 1 | 0  2 1  0 | *  *  * * 36 * *   0  0  0  0  2  4 |  0  0  0  8  2  2 | 0 0  4  4
... ... .o.3.x. ...       | 0 3 | 0  0 0  3 | *  *  * *  * 4 *   0  0  6  0  0  0 |  0  6  0  0  6  0 | 2 0  6  0
... ... ... .x.3.o.       | 0 3 | 0  0 0  3 | *  *  * *  * * 4   0  0  0  6  0  0 |  0  0  6  0  0  6 | 0 2  0  6
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. ... ... ...&#x  &  3 1 | 3  3 0  0 | 1  3  0 0  0 0 0 | 12  *  *  *  *  * |  4  0  0  0  0  0 | 2 2  0  0
xo. ... ... ox. ...&#x  &  2 2 | 1  4 0  1 | 0  2  2 0  0 0 0 |  * 72  *  *  *  * |  1  1  1  1  0  0 | 1 1  1  1
... ... oo.3ox. ...&#x  &  1 3 | 0  3 0  3 | 0  0  3 0  0 1 0 |  *  * 24  *  *  * |  0  2  0  0  2  0 | 1 0  3  0
... ... ... ox.3oo.&#x  &  1 3 | 0  3 0  3 | 0  0  3 0  0 0 1 |  *  *  * 24  *  * |  0  0  2  0  0  2 | 0 1  0  3
xoo ... ... ... ...&#x  &  3 1 | 1  3 2  0 | 0  1  0 1  2 0 0 |  *  *  *  * 36  * |  0  0  0  4  0  0 | 0 0  2  2
... ... ... oxo ...&#x     2 2 | 0  4 1  1 | 0  0  2 0  2 0 0 |  *  *  *  *  * 72 |  0  0  0  2  1  1 | 0 0  2  2
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. ... ox. ...&#x  &  3 2 | 3  6 0  1 | 1  6  3 0  0 0 0 |  2  3  0  0  0  0 | 24  *  *  *  *  * | 1 1  0  0
xo. ... oo.3ox. ...&#x  &  2 3 | 1  6 0  3 | 0  3  6 0  0 1 0 |  0  3  2  0  0  0 |  * 24  *  *  *  * | 1 0  1  0
xo. ... ... ox.3oo.&#x  &  2 3 | 1  6 0  3 | 0  3  6 0  0 0 1 |  0  3  0  2  0  0 |  *  * 24  *  *  * | 0 1  0  1
xoo ... ... oxo ...&#x  &  3 2 | 1  6 2  1 | 0  2  3 1  4 0 0 |  0  1  0  0  2  2 |  *  *  * 72  *  * | 0 0  1  1
... ... ooo3oxo ...&#x     2 3 | 0  6 1  3 | 0  0  6 0  3 1 0 |  0  0  2  0  0  3 |  *  *  *  * 24  * | 0 0  2  0
... ... ... oxo3ooo&#x     2 3 | 0  6 1  3 | 0  0  6 0  3 0 1 |  0  0  0  2  0  3 |  *  *  *  *  * 24 | 0 0  0  2
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. oo.3ox. ...&#x  &  3 3 | 3  9 0  3 | 1  9  9 0  0 1 0 |  3  9  3  0  0  0 |  3  3  0  0  0  0 | 8 *  *  *
xo.3oo. ... ox.3oo.&#x  &  3 3 | 3  9 0  3 | 1  9  9 0  0 0 1 |  3  9  0  3  0  0 |  3  0  3  0  0  0 | * 8  *  *
xoo ... ooo3oxo ...&#x  &  3 3 | 1  9 2  3 | 0  3  9 1  6 1 0 |  0  3  3  0  3  6 |  0  1  0  3  2  0 | * * 24  *
xoo ... ... oxo3ooo&#x  &  3 3 | 1  9 2  3 | 0  3  9 1  6 0 1 |  0  3  0  3  3  6 |  0  0  1  3  0  2 | * *  * 24

xo3oo4oo ox3oo4oo&#zx   → height = 0
(tegum sum of 2 perp octs)
(tegum product of 2 octs)

o.3o.4o. o.3o.4o.    | 6 *   4  6  0 | 4 24 12 0 | 24  48  8 | 48 32 | 32
.o3.o4.o .o3.o4.o    | * 6   0  6  4 | 0 12 24 4 |  8  48 24 | 32 48 | 32
---------------------+-----+----------+-----------+-----------+-------+---
x. .. .. .. .. ..    | 2 0 | 12  *  *  2  6  0 0 | 12  12  0 | 24  8 | 16
oo3oo4oo oo3oo4oo&#x | 1 1 |  * 36  *  0  4  4 0 |  4  16  4 | 16 16 | 16
.. .. .. .x .. ..    | 0 2 |  *  * 12  0  0  6 2 |  0  12 12 |  8 24 | 16
---------------------+-----+----------+-----------+-----------+-------+---
x.3o. .. .. .. ..    | 3 0 |  3  0  0 | 8  *  * *   6   0  0 | 12  0 |  8
xo .. .. .. .. ..&#x | 2 1 |  1  2  0 | * 72  * *   2   4  0 |  8  4 |  8
.. .. .. ox .. ..&#x | 1 2 |  0  2  1 | *  * 72 *   0   4  2 |  4  8 |  8
.. .. .. .x3.o ..    | 0 3 |  0  0  3 | *  *  * 8   0   0  6 |  0 12 |  8
---------------------+-----+----------+-----------+-----------+-------+---
xo3oo .. .. .. ..&#x  3 1 |  3  3  0 | 1  3  0 0 | 48   *  * |  4  0 |  4
xo .. .. ox .. ..&#x  2 2 |  1  4  1 | 0  2  2 0 |  * 144  * |  2  2 |  4
.. .. .. ox3oo ..&#x  1 3 |  0  3  3 | 0  0  3 1 |  *   * 48 |  0  4 |  4
---------------------+-----+----------+-----------+-----------+-------+---
xo3oo .. ox .. ..&#x  3 2 |  3  6  1 | 1  6  3 0 |  2   3  0 | 96  * |  2
xo .. .. ox3oo ..&#x  2 3 |  1  6  3 | 0  3  6 1 |  0   3  2 |  * 96 |  2
---------------------+-----+----------+-----------+-----------+-------+---
xo3oo .. ox3oo ..&#x  3 3 |  3  9  3 | 1  9  9 1 |  3   9  3 |  3  3 | 64
or
o.3o.4o. o.3o.4o.    & | 12   4  6 |  4  36 | 32  48 |  80 | 32
-----------------------+----+-------+--------+--------+-----+---
x. .. .. .. .. ..    & |  2 | 24  *   2   6 | 12  12 |  32 | 16
oo3oo4oo oo3oo4oo&#x   |  2 |  * 36   0   8 |  8  16 |  32 | 16
-----------------------+----+-------+--------+--------+-----+---
x.3o. .. .. .. ..    & |  3 |  3  0 | 16   *   6   0 |  12 |  8
xo .. .. .. .. ..&#x & |  3 |  1  2 |  * 144   2   4 |  12 |  8
-----------------------+----+-------+--------+--------+-----+---
xo3oo .. .. .. ..&#x &   4 |  3  3 |  1   3 | 96   * |   4 |  4
xo .. .. ox .. ..&#x     4 |  2  4 |  0   4 |  * 144 |   4 |  4
-----------------------+----+-------+--------+--------+-----+---
xo3oo .. ox .. ..&#x &   5 |  4  6 |  1   9 |  2   3 | 192 |  2
-----------------------+----+-------+--------+--------+-----+---
xo3oo .. ox3oo ..&#x     6 |  6  9 |  2  18 |  6   9 |   6 | 64

oo3xo3oo oo3ox3oo&#zx   → height = 0
(tegum sum of 2 perp octs)
(tegum product of 2 octs)

o.3o.3o. o.3o.3o.    & | 12   4  6 | 2 2  36 | 16 16  48 | 40 40 | 16  8  8
-----------------------+----+-------+---------+-----------+-------+---------
.. x.. .. .. .. ..   & |  2 | 24  *  1 1   6 |  6  6  12 | 16 16 |  8  4  4
oo3oo3oo oo3oo3oo&#x   |  2 |  * 36  0 0   8 |  4  4  16 | 16 16 |  8  4  4
-----------------------+----+-------+---------+-----------+-------+---------
o.3x. .. .. .. ..    & |  3 |  3  0 | 8 *   *   6  0   0 | 12  0 |  4  4  0
.. x.3o. .. .. ..    & |  3 |  3  0 | * 8   *   0  6   0 |  0 12 |  4  0  4
.. xo .. .. .. ..&#x & |  3 |  1  2 | * * 144   1  1   4 |  6  6 |  4  2  2
-----------------------+----+-------+---------+-----------+-------+---------
oo3xo .. .. .. ..&#x &   4 |  3  3 | 1 0   3 | 48  *   * |  4  0 |  2  2  0
.. xo3oo .. .. ..&#x &   4 |  3  3 | 0 1   3 |  * 48   * |  0  4 |  2  0  2
.. xo .. .. ox ..&#x     4 |  2  4 | 0 0   4 |  *  * 144 |  2  2 |  2  1  1
-----------------------+----+-------+---------+-----------+-------+---------
oo3xo .. .. ox ..&#x &   5 |  4  6 | 1 0   9 |  2  0   3 | 96  * |  1  1  0
.. xo3oo .. ox ..&#x &   5 |  4  6 | 0 1   9 |  0  2   3 |  * 96 |  1  0  1
-----------------------+----+-------+---------+-----------+-------+---------
oo3xo .. oo3ox ..&#x &   6 |  6  9 | 1 1  18 |  3  3   9 |  3  3 | 32  *  *
oo3xo .. .. ox3oo&#x     6 |  6  9 | 2 0  18 |  6  0   9 |  6  0 |  * 16  *
.. xo3oo oo3ox ..&#x     6 |  6  9 | 0 2  18 |  0  6   9 |  0  6 |  *  * 16

xooo3ooxo oxoo3ooox&#xr   → all cyclical heights = 1/sqrt(3) = 0.577350
                            (in fact this lace simplex degenerates into a square)

... 

xoo4ooo oxo4ooo oox4ooo&#zx   → all heights = 0
(tegum sum of 3 pairwise orthogonal {4})
(tegum product of 3 {4})

o..4o.. o..4o.. o..4o..     & | 12   2  8 | 24 16 | 16  64 |  80 | 32
------------------------------+----+-------+-------+--------+-----+---
x.. ... ... ... ... ...     & |  2 | 12  *   8  0 |  8  16 |  32 | 16
oo.4oo. oo.4oo. oo.4oo.&#x  & |  2 |  * 48   4  4 |  4  20 |  32 | 16
------------------------------+----+-------+-------+--------+-----+---
xo. ... ... ... ... ...     & |  3 |  1  2 | 96  *   2   4 |  12 |  8
ooo4ooo ooo4ooo ooo4ooo&#x  & |  3 |  0  3 |  * 64   0   6 |  12 |  8
------------------------------+----+-------+-------+--------+-----+---
xo. ... ox. ... ... ...&#x  &   4 |  2  4 |  4  0 | 48   * |   4 |  4
xoo ... ... ... ... ...&#x  &   4 |  1  5 |  2  2 |  * 192 |   4 |  4
------------------------------+----+-------+-------+--------+-----+---
xoo ... oxo ... ... ...&#x  &   5 |  2  8 |  6  4 |  1   4 | 192 |  2
------------------------------+----+-------+-------+--------+-----+---
xoo ... oxo ... oox ...&#x  &   6 |  3 12 | 12  8 |  3  12 |   6 | 64

xoo xoo oxo oxo oox oox&#zx   → all heights = 0
(tegum sum of 3 pairwise orthogonal {4})
(tegum product of 3 {4})

o.. o.. o.. o.. o.. o..     & | 12   2  8 | 24 16 | 16  64 |  80 | 32
------------------------------+----+-------+-------+--------+-----+---
x.. ... ... ... ... ...     & |  2 | 12  *   8  0 |  8  16 |  32 | 16
oo. oo. oo. oo. oo. oo.&#x  & |  2 |  * 48   4  4 |  4  20 |  32 | 16
------------------------------+----+-------+-------+--------+-----+---
xo. ... ... ... ... ...     & |  3 |  1  2 | 96  *   2   4 |  12 |  8
ooo ooo ooo ooo ooo ooo&#x  & |  3 |  0  3 |  * 64   0   6 |  12 |  8
------------------------------+----+-------+-------+--------+-----+---
xo. ... ox. ... ... ...&#x  &   4 |  2  4 |  4  0 | 48   * |   4 |  4
xoo ... ... ... ... ...&#x  &   4 |  1  5 |  2  2 |  * 192 |   4 |  4
------------------------------+----+-------+-------+--------+-----+---
xoo ... oxo ... ... ...&#x  &   5 |  2  8 |  6  4 |  1   4 | 192 |  2
------------------------------+----+-------+-------+--------+-----+---
xoo ... oxo ... oox ...&#x  &   6 |  3 12 | 12  8 |  3  12 |   6 | 64

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