Acronym tac
Name triacontiditeron,
pentacross5),
aeropet(id),
pentachoral antiprism,
vertex figure of gee
Field of sections
 ©
Circumradius 1/sqrt(2) = 0.707107
Inradius 1/sqrt(10) = 0.316228
Vertex figure
 ©
Lace city
in approx. ASCII-art
o3o3o   x3o3o  
               
               
               
  o3o3x   o3o3o
x o3o   o x3o 
              
              
              
              
 o o3x   x o3o
Coordinates (1/sqrt(2), 0, 0, 0, 0)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: hexpen
hehad 516
tac 032
& others)
Dual pent
Dihedral angles
  • at tet between pen and pen:   arccos(-3/5) = 126.869898°
Confer
related segmentotera:
hexpy   squete  
general polytopal classes:
orthoplex   partial Stott expansions   segmentotera   fundamental lace prisms  
External
links
hedrondude   wikipedia

Incidence matrix according to Dynkin symbol

x3o3o3o4o

. . . . . | 10   8 | 24 | 32 | 16
----------+----+----+----+----+---
x . . . . |  2 | 40   6 | 12 |  8
----------+----+----+----+----+---
x3o . . . |  3 |  3 | 80 |  4 |  4
----------+----+----+----+----+---
x3o3o . .   4 |  6 |  4 | 80 |  2
----------+----+----+----+----+---
x3o3o3o .   5 | 10 | 10 |  5 | 32

x3o3o3o4/3o

. . . .   . | 10   8 | 24 | 32 | 16
------------+----+----+----+----+---
x . . .   . |  2 | 40   6 | 12 |  8
------------+----+----+----+----+---
x3o . .   . |  3 |  3 | 80 |  4 |  4
------------+----+----+----+----+---
x3o3o .   .   4 |  6 |  4 | 80 |  2
------------+----+----+----+----+---
x3o3o3o   .   5 | 10 | 10 |  5 | 32

o3o3o *b3o3x

. . .    . . | 10   8 | 24 | 32 |  8  8
-------------+----+----+----+----+------
. . .    . x |  2 | 40   6 | 12 |  4  4
-------------+----+----+----+----+------
. . .    o3x |  3 |  3 | 80 |  4 |  2  2
-------------+----+----+----+----+------
. o . *b3o3x   4 |  6 |  4 | 80 |  1  1
-------------+----+----+----+----+------
o3o . *b3o3x   5 | 10 | 10 |  5 | 16  *
. o3o *b3o3x   5 | 10 | 10 |  5 |  * 16

xo3oo3oo3ox&#x   → height = sqrt(2/5) = 0.632456
(pen || dual pen)

o.3o.3o.3o.    | 5 *   4  4  0 |  6 12  6  0 | 4 12 12  4 0 | 1 4  6  4 1 0
.o3.o3.o3.o    | * 5   0  4  4 |  0  6 12  6 | 0  4 12 12 4 | 0 1  4  6 4 1
---------------+-----+----------+-------------+--------------+--------------
x. .. .. ..    | 2 0 | 10  *  *   3  3  0  0 | 3  6  3  0 0 | 1 3  3  1 0 0
oo3oo3oo3oo&#x | 1 1 |  * 20  *   0  3  3  0 | 0  3  6  3 0 | 0 1  3  3 1 0
.. .. .. .x    | 0 2 |  *  * 10   0  0  3  3 | 0  0  3  6 3 | 0 0  1  3 3 1
---------------+-----+----------+-------------+--------------+--------------
x.3o. .. ..    | 3 0 |  3  0  0 | 10  *  *  * | 2  2  0  0 0 | 1 2  1  0 0 0
xo .. .. ..&#x | 2 1 |  1  2  0 |  * 30  *  * | 0  2  2  0 0 | 0 1  2  1 0 0
.. .. .. ox&#x | 1 2 |  0  2  1 |  *  * 30  * | 0  0  2  2 0 | 0 0  1  2 1 0
.. .. .o3.x    | 0 3 |  0  0  3 |  *  *  * 10 | 0  0  0  2 2 | 0 0  0  1 2 1
---------------+-----+----------+-------------+--------------+--------------
x.3o.3o. ..     4 0 |  6  0  0 |  4  0  0  0 | 5  *  *  * * | 1 1  0  0 0 0
xo3oo .. ..&#x  3 1 |  3  3  0 |  1  3  0  0 | * 20  *  * * | 0 1  1  0 0 0
xo .. .. ox&#x  2 2 |  1  4  1 |  0  2  2  0 | *  * 30  * * | 0 0  1  1 0 0
.. .. oo3ox&#x  1 3 |  0  3  3 |  0  0  3  1 | *  *  * 20 * | 0 0  0  1 1 0
.. .o3.o3.x     0 4 |  0  0  6 |  0  0  0  4 | *  *  *  * 5 | 0 0  0  0 1 1
---------------+-----+----------+-------------+--------------+--------------
x.3o.3o.3o.     5 0 | 10  0  0 | 10  0  0  0 | 5  0  0  0 0 | 1 *  *  * * *
xo3oo3oo ..&#x  4 1 |  6  4  0 |  4  6  0  0 | 1  4  0  0 0 | * 5  *  * * *
xo3oo .. ox&#x  3 2 |  3  6  1 |  1  6  3  0 | 0  2  3  0 0 | * * 10  * * *
xo .. oo3ox&#x  2 3 |  1  6  3 |  0  3  6  1 | 0  0  3  2 0 | * *  * 10 * *
.. oo3oo3ox&#x  1 4 |  0  4  6 |  0  0  6  4 | 0  0  0  4 1 | * *  *  * 5 *
.o3.o3.o3.x     0 5 |  0  0 10 |  0  0  0 10 | 0  0  0  0 5 | * *  *  * * 1
or
o.3o.3o.3o.    & | 10   4  4 |  6 18 |  4 16 12 | 1  5 10
-----------------+----+-------+-------+----------+--------
x. .. .. ..    & |  2 | 20  *   3  3 |  3  6  3 | 1  3  4
oo3oo3oo3oo&#x   |  2 |  * 20   0  6 |  0  6  6 | 0  2  6
-----------------+----+-------+-------+----------+--------
x.3o. .. ..    & |  3 |  3  0 | 20  * |  2  2  0 | 1  2  1
xo .. .. ..&#x & |  3 |  1  2 |  * 60 |  0  2  2 | 0  1  3
-----------------+----+-------+-------+----------+--------
x.3o.3o. ..    &   4 |  6  0 |  4  0 | 10  *  * | 1  1  0
xo3oo .. ..&#x &   4 |  3  3 |  1  3 |  * 40  * | 0  1  1
xo .. .. ox&#x     4 |  2  4 |  0  4 |  *  * 30 | 0  0  2
-----------------+----+-------+-------+----------+--------
x.3o.3o.3o.    &   5 | 10  0 | 10  0 |  5  0  0 | 2  *  *
xo3oo3oo ..&#x &   5 |  6  4 |  4  6 |  1  4  0 | * 10  *
xo3oo .. ox&#x &   5 |  4  6 |  1  9 |  0  2  3 | *  * 20

oxo3ooo3ooo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(pt || pseudo hex || pt)

o..3o..3o..4o..    | 1 * *  8  0 0 | 24  0  0 | 32  0  0 | 16  0
.o.3.o.3.o.4.o.    | * 8 *  1  6 1 |  6 12  6 | 12  8 12 |  8  8
..o3..o3..o4..o    | * * 1  0  0 8 |  0  0 24 |  0  0 32 |  0 16
-------------------+-------+--------+----------+----------+------
oo.3oo.3oo.4oo.&#x | 1 1 0 | 8  * *   6  0  0 | 12  0  0 |  8  0
.x. ... ... ...    | 0 2 0 | * 24 *   1  4  1 |  4  4  4 |  4  4
.oo3.oo3.oo4.oo&#x | 0 1 1 | *  * 8   0  0  6 |  0  0 12 |  0  8
-------------------+-------+--------+----------+----------+------
ox. ... ... ...&#x | 1 2 0 | 2  1 0 | 24  *  * |  4  0  0 |  4  0
.x.3.o. ... ...    | 0 3 0 | 0  3 0 |  * 32  * |  1  2  1 |  2  2
.xo ... ... ...&#x | 0 2 1 | 0  1 2 |  *  * 24 |  0  0  4 |  0  4
-------------------+-------+--------+----------+----------+------
ox.3oo. ... ...&#x  1 3 0 | 3  3 0 |  3  1  0 | 32  *  * |  2  0
.x.3.o.3.o. ...     0 4 0 | 0  6 0 |  0  4  0 |  * 16  * |  1  1
.xo3.oo ... ...&#x  0 3 1 | 0  3 3 |  0  1  3 |  *  * 32 |  0  2
-------------------+-------+--------+----------+----------+------
ox.3oo.3oo. ...&#x  1 4 0 | 4  6 0 |  6  4  0 |  4  1  0 | 16  *
.xo3.oo3.oo ...&#x  0 4 1 | 0  6 4 |  0  4  6 |  0  1  4 |  * 16
or
o..3o..3o..4o..    & | 2 *   8  0 | 24  0 | 32  0 | 16
.o.3.o.3.o.4.o.      | * 8   2  6 | 12 12 | 24  8 | 16
---------------------+-----+-------+-------+-------+---
oo.3oo.3oo.4oo.&#x & | 1 1 | 16  *   6  0 | 12  0 |  8
.x. ... ... ...      | 0 2 |  * 24   2  4 |  8  4 |  8
---------------------+-----+-------+-------+-------+---
ox. ... ... ...&#x & | 1 2 |  2  1 | 48  * |  4  0 |  4
.x.3.o. ... ...      | 0 3 |  0  3 |  * 32 |  2  2 |  4
---------------------+-----+-------+-------+-------+---
ox.3oo. ... ...&#x &  1 3 |  3  3 |  3  1 | 64  * |  2
.x.3.o.3.o. ...       0 4 |  0  6 |  0  4 |  * 16 |  2
---------------------+-----+-------+-------+-------+---
ox.3oo.3oo. ...&#x &  1 4 |  4  6 |  6  4 |  4  1 | 32

qo ox3oo3oo4oo&#zx   → height = 0
(tegum sum of q-line and perp hex)
(tegum product of q-line with hex)

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

oxo3ooo3ooo *b3ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(pt || pseudo hex || pt)

o..3o..3o.. *b3o..    | 1 * *  8  0 0 | 24  0  0 | 32 0 0  0 | 8 8 0 0
.o.3.o.3.o. *b3.o.    | * 8 *  1  6 1 |  6 12  6 | 12 4 4 12 | 4 4 4 4
..o3..o3..o *b3..o    | * * 1  0  0 8 |  0  0 24 |  0 0 0 32 | 0 0 8 8
----------------------+-------+--------+----------+-----------+--------
oo.3oo.3oo. *b3oo.&#x | 1 1 0 | 8  * *   6  0  0 | 12 0 0  0 | 4 4 0 0
.x. ... ...    ...    | 0 2 0 | * 24 *   1  4  1 |  4 2 2  4 | 2 2 2 2
.oo3.oo3.oo *b3.oo&#x | 0 1 1 | *  * 8   0  0  6 |  0 0 0 12 | 0 0 4 4
----------------------+-------+--------+----------+-----------+--------
ox. ... ...    ...&#x | 1 2 0 | 2  1 0 | 24  *  * |  4 0 0  0 | 2 2 0 0
.x.3.o. ...    ...    | 0 3 0 | 0  3 0 |  * 32  * |  1 1 1  1 | 1 1 1 1
.xo ... ...    ...&#x | 0 2 1 | 0  1 2 |  *  * 24 |  0 0 0  4 | 0 0 2 2
----------------------+-------+--------+----------+-----------+--------
ox.3oo. ...    ...&#x  1 3 0 | 3  3 0 |  3  1  0 | 32 * *  * | 1 1 0 0
.x.3.o.3.o.    ...     0 4 0 | 0  6 0 |  0  4  0 |  * 8 *  * | 1 0 1 0
.x.3.o. ... *b3.o.     0 4 0 | 0  6 0 |  0  4  0 |  * * 8  * | 0 1 0 1
.xo3.oo ...    ...&#x  0 3 1 | 0  3 3 |  0  1  3 |  * * * 32 | 0 0 1 1
----------------------+-------+--------+----------+-----------+--------
ox.3oo.3oo.    ...&#x  1 4 0 | 4  6 0 |  6  4  0 |  4 1 0  0 | 8 * * *
ox.3oo. ... *b3oo.&#x  1 4 0 | 4  6 0 |  6  4  0 |  4 0 1  0 | * 8 * *
.xo3.oo3.oo    ...&#x  0 4 1 | 0  6 4 |  0  4  6 |  0 1 0  4 | * * 8 *
.xo3.oo ... *b3.oo&#x  0 4 1 | 0  6 4 |  0  4  6 |  0 0 1  4 | * * * 8
or
o..3o..3o.. *b3o..    & | 2 *   8  0 | 24  0 | 32 0 0 |  8  8
.o.3.o.3.o. *b3.o.      | * 8   2  6 | 12 12 | 24 4 4 |  8  8
------------------------+-----+-------+-------+--------+------
oo.3oo.3oo. *b3oo.&#x & | 1 1 | 16  *   6  0 | 12 0 0 |  4  4
.x. ... ...    ...      | 0 2 |  * 24   2  4 |  8 2 2 |  4  4
------------------------+-----+-------+-------+--------+------
ox. ... ...    ...&#x & | 1 2 |  2  1 | 48  * |  4 0 0 |  2  2
.x.3.o. ...    ...      | 0 3 |  0  3 |  * 32 |  2 1 1 |  2  2
------------------------+-----+-------+-------+--------+------
ox.3oo. ...    ...&#x &  1 3 |  3  3 |  3  1 | 64 * * |  1  1
.x.3.o.3.o.    ...       0 4 |  0  6 |  0  4 |  * 8 * |  2  0
.x.3.o. ... *b3.o.       0 4 |  0  6 |  0  4 |  * * 8 |  0  2
------------------------+-----+-------+-------+--------+------
ox.3oo.3oo.    ...&#x &  1 4 |  4  6 |  6  4 |  4 1 0 | 16  *
ox.3oo. ... *b3oo.&#x &  1 4 |  4  6 |  6  4 |  4 0 1 |  * 16

qo ox3oo3oo *b3oo&#zx   → height = 0
(tegum sum of q-line and perp hex)
(tegum product of q-line with hex)

o. o.3o.3o. *b3o.    | 2 *   8  0 | 24  0 | 32 0 0 |  8  8
.o .o3.o3.o *b3.o    | * 8   2  6 | 12 12 | 24 4 4 |  8  8
---------------------+-----+-------+-------+--------+------
oo oo3oo3oo *b3oo&#x | 1 1 | 16  *   6  0 | 12 0 0 |  4  4
.. .x .. ..    ..    | 0 2 |  * 24   2  4 |  8 2 2 |  4  4
---------------------+-----+-------+-------+--------+------
.. ox .. ..    ..&#x | 1 2 |  2  1 | 48  * |  4 0 0 |  2  2
.. .x3.o ..    ..    | 0 3 |  0  3 |  * 32 |  2 1 1 |  2  2
---------------------+-----+-------+-------+--------+------
.. ox3oo ..    ..&#x  1 3 |  3  3 |  3  1 | 64 * * |  1  1
.. .x3.o3.o    ..     0 4 |  0  6 |  0  4 |  * 8 * |  2  0
.. .x3.o .. *b3.o     0 4 |  0  6 |  0  4 |  * * 8 |  0  2
---------------------+-----+-------+-------+--------+------
.. ox3oo3oo    ..&#x  1 4 |  4  6 |  6  4 |  4 1 0 | 16  *
.. ox3oo .. *b3oo&#x  1 4 |  4  6 |  6  4 |  4 0 1 |  * 16

xox oxo3ooo4ooo&#xt   → both heights = 1/2
(line || perp pseudo oct || line)

o.. o..3o..4o..    | 2 * *  1  6 1  0  0 0 | 6 12  6 0 0  0 | 12  8 12  0  0 | 8  8 0
.o. .o.3.o.4.o.    | * 6 *  0  2 0  4  2 0 | 1  8  2 4 1  8 |  4  8  8  4  8 | 4  8 4
..o ..o3..o4..o    | * * 2  0  0 1  0  6 1 | 0  0  6 0 6 12 |  0  0 12 12  8 | 0  8 8
-------------------+-------+----------------+----------------+----------------+-------
x.. ... ... ...    | 2 0 0 | 1  * *  *  * *  6  0  0 0 0  0 | 12  0  0  0  0 | 8  0 0
oo. oo.3oo.4oo.&#x | 1 1 0 | * 12 *  *  * *  1  4  1 0 0  0 |  4  4  4  0  0 | 4  4 0
o.o o.o3o.o4o.o&#x | 1 0 1 | *  * 2  *  * *  0  0  6 0 0  0 |  0  0 12  0  0 | 0  8 0
... .x. ... ...    | 0 2 0 | *  * * 12  * *  0  2  0 2 0  2 |  1  4  2  1  4 | 2  4 2
.oo .oo3.oo4.oo&#x | 0 1 1 | *  * *  * 12 *  0  0  1 0 1  4 |  0  0  4  4  4 | 0  4 4
..x ... ... ...    | 0 0 2 | *  * *  *  * 1  0  0  0 0 6  0 |  0  0  0 12  0 | 0  0 8
-------------------+-------+----------------+----------------+----------------+-------
xo. ... ... ...&#x | 2 1 0 | 1  2 0  0  0 0 | 6  *  * * *  * |  4  0  0  0  0 | 4  0 0
... ox. ... ...&#x | 1 2 0 | 0  2 0  1  0 0 | * 24  * * *  * |  1  2  1  0  0 | 2  2 0
ooo ooo3ooo4ooo&#x | 1 1 1 | 0  1 1  0  1 0 | *  * 12 * *  * |  0  0  4  0  0 | 0  4 0
... .x.3.o. ...    | 0 3 0 | 0  0 0  3  0 0 | *  *  * 8 *  * |  0  2  0  0  2 | 1  2 1
.ox ... ... ...&#x | 0 1 2 | 0  0 0  0  2 1 | *  *  * * 6  * |  0  0  0  4  0 | 0  0 4
... .xo ... ...&#x | 0 2 1 | 0  0 0  1  2 0 | *  *  * * * 24 |  0  0  1  1  2 | 0  2 2
-------------------+-------+----------------+----------------+----------------+-------
xo. ox. ... ...&#x  2 2 0 | 1  4 0  1  0 0 | 2  2  0 0 0  0 | 12  *  *  *  * | 2  0 0
... ox.3oo. ...&#x  1 3 0 | 0  3 0  3  0 0 | 0  3  0 1 0  0 |  * 16  *  *  * | 1  1 0
... oxo ... ...&#x  1 2 1 | 0  2 1  1  2 0 | 0  1  2 0 0  1 |  *  * 24  *  * | 0  2 0
.ox .xo ... ...&#x  0 2 2 | 0  0 0  1  4 1 | 0  0  0 0 2  2 |  *  *  * 12  * | 0  0 2
... .xo3.oo ...&#x  0 3 1 | 0  0 0  3  3 0 | 0  0  0 1 0  3 |  *  *  *  * 16 | 0  1 1
-------------------+-------+----------------+----------------+----------------+-------
xo. ox.3oo. ...&#x  2 3 0 | 1  6 0  3  0 0 | 3  6  0 1 0  0 |  3  2  0  0  0 | 8  * *
... oxo3ooo ...&#x  1 3 1 | 0  3 1  3  3 0 | 0  3  3 1 0  3 |  0  1  3  0  1 | * 16 *
.ox .xo3.oo ...&#x  0 3 2 | 0  0 0  3  6 1 | 0  0  0 1 3  6 |  0  0  0  3  2 | *  * 8
or
o.. o..3o..4o..     & | 4 *  1  6 1  0 |  6 12  6 0 | 12  8 12 |  8  8
.o. .o.3.o.4.o.       | * 6  0  4 0  4 |  2 16  2 4 |  8 16  8 |  8  8
----------------------+-----+-----------+------------+----------+------
x.. ... ... ...     & | 2 0 | 2  * *  *   6  0  0 0 | 12  0  0 |  8  0
oo. oo.3oo.4oo.&#x  & | 1 1 | * 24 *  *   1  4  1 0 |  4  4  4 |  4  4
o.o o.o3o.o4o.o&#x    | 2 0 | *  * 2  *   0  0  6 0 |  0  0 12 |  0  8
... .x. ... ...       | 0 2 | *  * * 12   0  4  0 2 |  2  8  2 |  4  4
----------------------+-----+-----------+------------+----------+------
xo. ... ... ...&#x  & | 2 1 | 1  2 0  0 | 12  *  * * |  4  0  0 |  4  0
... ox. ... ...&#x  & | 1 2 | 0  2 0  1 |  * 48  * * |  1  2  1 |  2  2
ooo ooo3ooo4ooo&#x    | 2 1 | 0  2 1  0 |  *  * 12 * |  0  0  4 |  0  4
... .x.3.o. ...       | 0 3 | 0  0 0  3 |  *  *  * 8 |  0  4  0 |  2  2
----------------------+-----+-----------+------------+----------+------
xo. ox. ... ...&#x  &  2 2 | 1  4 0  1 |  2  2  0 0 | 24  *  * |  2  0
... ox.3oo. ...&#x  &  1 3 | 0  3 0  3 |  0  3  0 1 |  * 32  * |  1  1
... oxo ... ...&#x     2 2 | 0  4 1  1 |  0  2  2 0 |  *  * 24 |  0  2
----------------------+-----+-----------+------------+----------+------
xo. ox.3oo. ...&#x  &  2 3 | 1  6 0  3 |  3  6  0 1 |  3  2  0 | 16  *
... oxo3ooo ...&#x     2 3 | 0  6 1  3 |  0  6  3 1 |  0  2  3 |  * 16

xox ooo3oxo3ooo&#xt   → both heights = 1/2
(line || perp pseudo oct || line)

o.. o..3o..3o..    | 2 * *  1  6 1  0  0 0 | 6 12  6 0 0 0  0 | 12 4 4 12  0 0 0 | 4 4 4 4 0 0
.o. .o.3.o.3.o.    | * 6 *  0  2 0  4  2 0 | 1  8  2 2 2 1  8 |  4 4 4  8  4 4 4 | 2 2 4 4 2 2
..o ..o3..o3..o    | * * 2  0  0 1  0  6 1 | 0  0  6 0 0 6 12 |  0 0 0 12 12 4 4 | 0 0 4 4 4 4
-------------------+-------+----------------+------------------+------------------+------------
x.. ... ... ...    | 2 0 0 | 1  * *  *  * *  6  0  0 0 0 0  0 | 12 0 0  0  0 0 0 | 4 4 0 0 0 0
oo. oo.3oo.3oo.&#x | 1 1 0 | * 12 *  *  * *  1  4  1 0 0 0  0 |  4 2 2  4  0 0 0 | 2 2 2 2 0 0
o.o o.o3o.o3o.o&#x | 1 0 1 | *  * 2  *  * *  0  0  6 0 0 0  0 |  0 0 0 12  0 0 0 | 0 0 4 4 0 0
... ... .x. ...    | 0 2 0 | *  * * 12  * *  0  2  0 1 1 0  2 |  1 2 2  2  1 2 2 | 1 1 2 2 1 1
.oo .oo3.oo3.oo&#x | 0 1 1 | *  * *  * 12 *  0  0  1 0 0 1  4 |  0 0 0  4  4 2 2 | 0 0 2 2 2 2
..x ... ... ...    | 0 0 2 | *  * *  *  * 1  0  0  0 0 0 6  0 |  0 0 0  0 12 0 0 | 0 0 0 0 4 4
-------------------+-------+----------------+------------------+------------------+------------
xo. ... ... ...&#x | 2 1 0 | 1  2 0  0  0 0 | 6  *  * * * *  * |  4 0 0  0  0 0 0 | 2 2 0 0 0 0
... ... ox. ...&#x | 1 2 0 | 0  2 0  1  0 0 | * 24  * * * *  * |  1 1 1  1  0 0 0 | 1 1 1 1 0 0
ooo ooo3ooo3ooo&#x | 1 1 1 | 0  1 1  0  1 0 | *  * 12 * * *  * |  0 0 0  4  0 0 0 | 0 0 2 2 0 0
... .o.3.x. ...    | 0 3 0 | 0  0 0  3  0 0 | *  *  * 4 * *  * |  0 2 0  0  0 2 0 | 1 0 2 0 1 0
... ... .x.3.o.    | 0 3 0 | 0  0 0  3  0 0 | *  *  * * 4 *  * |  0 0 2  0  0 0 2 | 0 1 0 2 0 1
.ox ... ... ...&#x | 0 1 2 | 0  0 0  0  2 1 | *  *  * * * 6  * |  0 0 0  0  4 0 0 | 0 0 0 0 2 2
... ... .xo ...&#x | 0 2 1 | 0  0 0  1  2 0 | *  *  * * * * 24 |  0 0 0  1  1 1 1 | 0 0 1 1 1 1
-------------------+-------+----------------+------------------+------------------+------------
xo. ... ox. ...&#x  2 2 0 | 1  4 0  1  0 0 | 2  2  0 0 0 0  0 | 12 * *  *  * * * | 1 1 0 0 0 0
... oo.3ox. ...&#x  1 3 0 | 0  3 0  3  0 0 | 0  3  0 1 0 0  0 |  * 8 *  *  * * * | 1 0 1 0 0 0
... ... ox.3oo.&#x  1 3 0 | 0  3 0  3  0 0 | 0  3  0 0 1 0  0 |  * * 8  *  * * * | 0 1 0 1 0 0
... ... oxo ...&#x  1 2 1 | 0  2 1  1  2 0 | 0  1  2 0 0 0  1 |  * * * 24  * * * | 0 0 1 1 0 0
.ox ... .xo ...&#x  0 2 2 | 0  0 0  1  4 1 | 0  0  0 0 0 2  2 |  * * *  * 12 * * | 0 0 0 0 1 1
... .oo3.xo ...&#x  0 3 1 | 0  0 0  3  3 0 | 0  0  0 1 0 0  3 |  * * *  *  * 8 * | 0 0 1 0 1 0
... ... .xo3.oo&#x  0 3 1 | 0  0 0  3  3 0 | 0  0  0 0 1 0  3 |  * * *  *  * * 8 | 0 0 0 1 0 1
-------------------+-------+----------------+------------------+------------------+------------
xo. oo.3ox. ...&#x  2 3 0 | 1  6 0  3  0 0 | 3  6  0 1 0 0  0 |  3 2 0  0  0 0 0 | 4 * * * * *
xo. ... ox.3oo.&#x  2 3 0 | 1  6 0  3  0 0 | 3  6  0 0 1 0  0 |  3 0 2  0  0 0 0 | * 4 * * * *
... ooo3oxo ...&#x  1 3 1 | 0  3 1  3  3 0 | 0  3  3 1 0 0  3 |  0 1 0  3  0 1 0 | * * 8 * * *
... ... oxo3ooo&#x  1 3 1 | 0  3 1  3  3 0 | 0  3  3 0 1 0  3 |  0 0 1  3  0 0 1 | * * * 8 * *
.ox .oo3.xo ...&#x  0 3 2 | 0  0 0  3  6 1 | 0  0  0 1 0 3  6 |  0 0 0  0  3 2 0 | * * * * 4 *
.ox ... .xo3.oo&#x  0 3 2 | 0  0 0  3  6 1 | 0  0  0 0 1 3  6 |  0 0 0  0  3 0 2 | * * * * * 4
or
o.. o..3o..3o..     & | 4 *  1  6 1  0 |  6 12  6 0 0 | 12  4  4 12 | 4 4 4 4
.o. .o.3.o.3.o.       | * 6  0  4 0  4 |  2 16  2 2 2 |  8  8  8  8 | 4 4 4 4
----------------------+-----+-----------+--------------+-------------+--------
x.. ... ... ...     & | 2 0 | 2  * *  *   6  0  0 0 0 | 12  0  0  0 | 4 4 0 0
oo. oo.3oo.3oo.&#x  & | 1 1 | * 24 *  *   1  4  1 0 0 |  4  2  2  4 | 2 2 2 2
o.o o.o3o.o3o.o&#x    | 2 0 | *  * 2  *   0  0  6 0 0 |  0  0  0 12 | 0 0 4 4
... ... .x. ...       | 0 2 | *  * * 12   0  4  0 1 1 |  2  4  4  2 | 2 2 2 2
----------------------+-----+-----------+--------------+-------------+--------
xo. ... ... ...&#x  & | 2 1 | 1  2 0  0 | 12  *  * * * |  4  0  0  0 | 2 2 0 0
... ... ox. ...&#x  & | 1 2 | 0  2 0  1 |  * 48  * * * |  1  1  1  1 | 1 1 1 1
ooo ooo3ooo3ooo&#x    | 2 1 | 0  2 1  0 |  *  * 12 * * |  0  0  0  4 | 0 0 2 2
... .o.3.x. ...       | 0 3 | 0  0 0  3 |  *  *  * 4 * |  0  4  0  0 | 2 0 2 0
... ... .x.3.o.       | 0 3 | 0  0 0  3 |  *  *  * * 4 |  0  0  4  0 | 0 2 0 2
----------------------+-----+-----------+--------------+-------------+--------
xo. ... ox. ...&#x  &  2 2 | 1  4 0  1 |  2  2  0 0 0 | 24  *  *  * | 1 1 0 0
... oo.3ox. ...&#x  &  1 3 | 0  3 0  3 |  0  3  0 1 0 |  * 16  *  * | 1 0 1 0
... ... ox.3oo.&#x  &  1 3 | 0  3 0  3 |  0  3  0 0 1 |  *  * 16  * | 0 1 0 1
... ... oxo ...&#x     2 2 | 0  4 1  1 |  0  2  2 0 0 |  *  *  * 24 | 0 0 1 1
----------------------+-----+-----------+--------------+-------------+--------
xo. oo.3ox. ...&#x  &  2 3 | 1  6 0  3 |  3  6  0 1 0 |  3  2  0  0 | 8 * * *
xo. ... ox.3oo.&#x  &  2 3 | 1  6 0  3 |  3  6  0 0 1 |  3  0  2  0 | * 8 * *
... ooo3oxo ...&#x     2 3 | 0  6 1  3 |  0  6  3 1 0 |  0  2  0  3 | * * 8 *
... ... oxo3ooo&#x     2 3 | 0  6 1  3 |  0  6  3 0 1 |  0  0  2  3 | * * * 8

xoo3oox oxo4ooo&#xt   → both heights = 1/sqrt(6) = 0.408248
({3} || perp pseudo {4} || dual {3})

o..3o.. o..4o..    | 3 * *  2  4 2 0  0 0 | 1  8  4 2 1  8  0  0 0 | 4  8  8  4  8 0  0 | 4  8  4 0
.o.3.o. .o.4.o.    | * 4 *  0  3 0 2  3 0 | 0  3  6 0 0  6  3  6 0 | 1  6  3  3 12 1  6 | 2  6  6 2
..o3..o ..o4..o    | * * 3  0  0 2 0  4 2 | 0  0  0 1 2  8  8  4 1 | 0  0  4  8  8 4  8 | 0  4  8 4
-------------------+-------+---------------+------------------------+--------------------+----------
x.. ... ... ...    | 2 0 0 | 3  * * *  * *  1  4  0 1 0  0  0  0 0 | 4  4  4  0  0 0  0 | 4  4  0 0
oo.3oo. oo.4oo.&#x | 1 1 0 | * 12 * *  * *  0  2  2 0 0  2  0  0 0 | 1  4  2  1  4 0  0 | 2  4  2 0
o.o3o.o o.o4o.o&#x | 1 0 1 | *  * 6 *  * *  0  0  0 1 1  4  0  0 0 | 0  0  4  4  4 0  0 | 0  4  4 0
... ... .x. ...    | 0 2 0 | *  * * 4  * *  0  0  3 0 0  0  0  3 0 | 0  3  0  0  6 0  3 | 1  3  3 1
.oo3.oo .oo4.oo&#x | 0 1 1 | *  * * * 12 *  0  0  0 0 0  2  2  2 0 | 0  0  1  2  4 1  4 | 0  2  4 2
... ..x ... ...    | 0 0 2 | *  * * *  * 3  0  0  0 0 1  0  4  0 1 | 0  0  0  4  0 4  4 | 0  0  4 4
-------------------+-------+---------------+------------------------+--------------------+----------
x..3o.. ... ...    | 3 0 0 | 3  0 0 0  0 0 | 1  *  * * *  *  *  * * | 4  0  0  0  0 0  0 | 4  0  0 0
xo. ... ... ...&#x | 2 1 0 | 1  2 0 0  0 0 | * 12  * * *  *  *  * * | 1  2  1  0  0 0  0 | 2  2  0 0
... ... ox. ...&#x | 1 2 0 | 0  2 0 1  0 0 | *  * 12 * *  *  *  * * | 0  2  0  0  2 0  0 | 1  2  1 0
x.o ... ... ...&#x | 2 0 1 | 1  0 2 0  0 0 | *  *  * 3 *  *  *  * * | 0  0  4  0  0 0  0 | 0  4  0 0
... o.x ... ...&#x | 1 0 2 | 0  0 2 0  0 1 | *  *  * * 3  *  *  * * | 0  0  0  4  0 0  0 | 0  0  4 0
ooo3ooo ooo4ooo&#x | 1 1 1 | 0  1 1 0  1 0 | *  *  * * * 24  *  * * | 0  0  1  1  2 0  0 | 0  2  2 0
... .ox ... ...&#x | 0 1 2 | 0  0 0 0  2 1 | *  *  * * *  * 12  * * | 0  0  0  1  0 1  2 | 0  0  2 2
... ... .xo ...&#x | 0 2 1 | 0  0 0 1  2 0 | *  *  * * *  *  * 12 * | 0  0  0  0  2 0  2 | 0  1  2 1
..o3..x ... ...    | 0 0 3 | 0  0 0 0  0 3 | *  *  * * *  *  *  * 1 | 0  0  0  0  0 4  0 | 0  0  0 4
-------------------+-------+---------------+------------------------+--------------------+----------
xo.3oo. ... ...&#x  3 1 0 | 3  3 0 0  0 0 | 1  3  0 0 0  0  0  0 0 | 4  *  *  *  * *  * | 2  0  0 0
xo. ... ox. ...&#x  2 2 0 | 1  4 0 1  0 0 | 0  2  2 0 0  0  0  0 0 | * 12  *  *  * *  * | 1  1  0 0
xoo ... ... ...&#x  2 1 1 | 1  2 2 0  1 0 | 0  1  0 1 0  2  0  0 0 | *  * 12  *  * *  * | 0  2  0 0
... oox ... ...&#x  1 1 2 | 0  1 2 0  2 1 | 0  0  0 0 1  2  1  0 0 | *  *  * 12  * *  * | 0  0  2 0
... ... oxo ...&#x  1 2 1 | 0  2 1 1  2 0 | 0  0  1 0 0  2  0  1 0 | *  *  *  * 24 *  * | 0  1  1 0
.oo3.ox ... ...&#x  0 1 3 | 0  0 0 0  3 3 | 0  0  0 0 0  0  3  0 1 | *  *  *  *  * 4  * | 0  0  0 2
... .ox .xo ...&#x  0 2 2 | 0  0 0 1  4 1 | 0  0  0 0 0  0  2  2 0 | *  *  *  *  * * 12 | 0  0  1 1
-------------------+-------+---------------+------------------------+--------------------+----------
xo.3oo. ox. ...&#x  3 2 0 | 3  6 0 1  0 0 | 1  6  3 0 0  0  0  0 0 | 2  3  0  0  0 0  0 | 4  *  * *
xoo ... oxo ...&#x  2 2 1 | 1  4 2 1  2 0 | 0  2  2 1 0  4  0  1 0 | 0  1  2  0  2 0  0 | * 12  * *
... oox oxo ...&#x  1 2 2 | 0  2 2 1  4 1 | 0  0  1 0 1  4  2  2 0 | 0  0  0  2  2 0  1 | *  * 12 *
.oo3.ox .xo ...&#x  0 2 3 | 0  0 0 1  6 3 | 0  0  0 0 0  0  6  3 1 | 0  0  0  0  0 2  3 | *  *  * 4
or
o..3o.. o..4o..    & | 6 *  2  4 2 0 | 1  8  4 3  8 | 4  8 12  8 | 4 12
.o.3.o. .o.4.o.      | * 4  0  6 0 2 | 0  6 12 0  6 | 2 12  6 12 | 4 12
---------------------+-----+----------+--------------+------------+-----
x.. ... ... ...    & | 2 0 | 6  * * *  1  4  0 1  0 | 4  4  4  0 | 4  4
oo.3oo. oo.4oo.&#x & | 1 1 | * 24 * *  0  2  2 0  2 | 1  4  3  4 | 2  6
o.o3o.o o.o4o.o&#x   | 2 0 | *  * 6 *  0  0  0 2  4 | 0  0  8  4 | 0  8
... ... .x. ...      | 0 2 | *  * * 4  0  0  6 0  0 | 0  6  0  6 | 2  6
---------------------+-----+----------+--------------+------------+-----
x..3o.. ... ...    & | 3 0 | 3  0 0 0 | 2  *  * *  * | 4  0  0  0 | 4  0
xo. ... ... ...&#x & | 2 1 | 1  2 0 0 | * 24  * *  * | 1  2  1  0 | 2  2
... ... ox. ...&#x & | 1 2 | 0  2 0 1 | *  * 24 *  * | 0  2  0  2 | 1  3
x.o ... ... ...&#x & | 3 0 | 1  0 2 0 | *  *  * 6  * | 0  0  4  0 | 0  4
ooo3ooo ooo4ooo&#x   | 2 1 | 0  2 1 0 | *  *  * * 24 | 0  0  2  2 | 0  4
---------------------+-----+----------+--------------+------------+-----
xo.3oo. ... ...&#x &  3 1 | 3  3 0 0 | 1  3  0 0  0 | 8  *  *  * | 2  0
xo. ... ox. ...&#x &  2 2 | 1  4 0 1 | 0  2  2 0  0 | * 24  *  * | 1  1
xoo ... ... ...&#x &  3 1 | 1  3 2 0 | 0  1  0 1  2 | *  * 24  * | 0  2
... ... oxo ...&#x    2 2 | 0  4 1 1 | 0  0  2 0  2 | *  *  * 24 | 0  2
---------------------+-----+----------+--------------+------------+-----
xo.3oo. ox. ...&#x &  3 2 | 3  6 0 1 | 1  6  3 0  0 | 2  3  0  0 | 8  *
xoo ... oxo ...&#x &  3 2 | 1  6 2 1 | 0  2  3 1  4 | 0  1  2  2 | * 24

oxo oxo xoo3oox&#xt   → both heights = 1/sqrt(6) = 0.408248
({3} || perp pseudo {4} || dual {3})

o.. o.. o..3o..    | 3 * *  2  4 2 0 0  0 0 | 1 2 2  8 2 1  8 0 0  0 0 | 4 4 4  4  4  8  4 0 0 0 | 2 2 4 2 4 2 0 0
.o. .o. .o.3.o.    | * 4 *  0  3 0 1 1  3 0 | 0 3 3  3 0 0  6 3 3  3 0 | 3 3 1  6  6  3  3 3 3 1 | 1 1 3 3 3 3 1 1
..o ..o ..o3..o    | * * 3  0  0 2 0 0  4 2 | 0 0 0  0 1 2  8 2 2  8 1 | 0 0 0  4  4  4  8 4 4 4 | 0 0 2 4 2 4 2 2
-------------------+-------+-----------------+--------------------------+-------------------------+----------------
... ... x.. ...    | 2 0 0 | 3  * * * *  * *  1 0 0  4 1 0  0 0 0  0 0 | 2 2 4  0  0  4  0 0 0 0 | 2 2 2 0 2 0 0 0
oo. oo. oo.3oo.&#x | 1 1 0 | * 12 * * *  * *  0 1 1  2 0 0  2 0 0  0 0 | 2 2 1  2  2  2  1 0 0 0 | 1 1 2 1 2 1 0 0
o.o o.o o.o3o.o&#x | 1 0 1 | *  * 6 * *  * *  0 0 0  0 1 1  4 0 0  0 0 | 0 0 0  2  2  4  4 0 0 0 | 0 0 2 2 2 2 0 0
.x. ... ... ...    | 0 2 0 | *  * * 2 *  * *  0 3 0  0 0 0  0 3 0  0 0 | 3 0 0  6  0  0  0 3 0 0 | 1 0 3 3 0 0 1 0
... .x. ... ...    | 0 2 0 | *  * * * 2  * *  0 0 3  0 0 0  0 0 3  0 0 | 0 3 0  0  6  0  0 0 3 0 | 0 1 0 0 3 3 0 1
.oo .oo .oo3.oo&#x | 0 1 1 | *  * * * * 12 *  0 0 0  0 0 0  2 1 1  2 0 | 0 0 0  2  2  1  2 2 2 1 | 0 0 1 2 1 2 1 1
... ... ... ..x    | 0 0 2 | *  * * * *  * 3  0 0 0  0 0 1  0 0 0  4 1 | 0 0 0  0  0  0  4 2 2 4 | 0 0 0 2 0 2 2 2
-------------------+-------+-----------------+--------------------------+-------------------------+----------------
... ... x..3o..    | 3 0 0 | 3  0 0 0 0  0 0 | 1 * *  * * *  * * *  * * | 0 0 4  0  0  0  0 0 0 0 | 2 2 0 0 0 0 0 0
ox. ... ... ...&#x | 1 2 0 | 0  2 0 1 0  0 0 | * 6 *  * * *  * * *  * * | 2 0 0  2  0  0  0 0 0 0 | 1 0 2 1 0 0 0 0
... ox. ... ...&#x | 1 2 0 | 0  2 0 0 1  0 0 | * * 6  * * *  * * *  * * | 0 2 0  0  2  0  0 0 0 0 | 0 1 0 0 2 1 0 0
... ... xo. ...&#x | 2 1 0 | 1  2 0 0 0  0 0 | * * * 12 * *  * * *  * * | 1 1 1  0  0  1  0 0 0 0 | 1 1 1 0 1 0 0 0
... ... x.o ...&#x | 2 0 1 | 1  0 2 0 0  0 0 | * * *  * 3 *  * * *  * * | 0 0 0  0  0  4  0 0 0 0 | 0 0 2 0 2 0 0 0
... ... ... o.x&#x | 1 0 2 | 0  0 2 0 0  0 1 | * * *  * * 3  * * *  * * | 0 0 0  0  0  0  4 0 0 0 | 0 0 0 2 0 2 0 0
ooo ooo ooo3ooo&#x | 1 1 1 | 0  1 1 0 0  1 0 | * * *  * * * 24 * *  * * | 0 0 0  1  1  1  1 0 0 0 | 0 0 1 1 1 1 0 0
.xo ... ... ...&#x | 0 2 1 | 0  0 0 1 0  2 0 | * * *  * * *  * 6 *  * * | 0 0 0  2  0  0  0 2 0 0 | 0 0 1 2 0 0 1 0
... .xo ... ...&#x | 0 2 1 | 0  0 0 0 1  2 0 | * * *  * * *  * * 6  * * | 0 0 0  0  2  0  0 0 2 0 | 0 0 0 0 1 2 0 1
... ... ... .ox&#x | 0 1 2 | 0  0 0 0 0  2 1 | * * *  * * *  * * * 12 * | 0 0 0  0  0  0  1 1 1 1 | 0 0 0 1 0 1 1 1
... ... ..o3..x    | 0 0 3 | 0  0 0 0 0  0 3 | * * *  * * *  * * *  * 1 | 0 0 0  0  0  0  0 0 0 4 | 0 0 0 0 0 0 2 2
-------------------+-------+-----------------+--------------------------+-------------------------+----------------
ox. ... xo. ...&#x  2 2 0 | 1  4 0 1 0  0 0 | 0 2 0  2 0 0  0 0 0  0 0 | 6 * *  *  *  *  * * * * | 1 0 1 0 0 0 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 | * 6 *  *  *  *  * * * * | 0 1 0 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 | * * 4  *  *  *  * * * * | 1 1 0 0 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 | * * * 12  *  *  * * * * | 0 0 1 1 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 | * * *  * 12  *  * * * * | 0 0 0 0 1 1 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 | * * *  *  * 12  * * * * | 0 0 1 0 1 0 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 | * * *  *  *  * 12 * * * | 0 0 0 1 0 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 | * * *  *  *  *  * 6 * * | 0 0 0 1 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 | * * *  *  *  *  * * 6 * | 0 0 0 0 0 1 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 | * * *  *  *  *  * * * 4 | 0 0 0 0 0 0 1 1
-------------------+-------+-----------------+--------------------------+-------------------------+----------------
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 | 3 0 2  0  0  0  0 0 0 0 | 2 * * * * * * *
... 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 3 2  0  0  0  0 0 0 0 | * 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 | 1 0 0  2  0  2  0 0 0 0 | * * 6 * * * * *
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 0 0  2  0  0  2 1 0 0 | * * * 6 * * * *
... 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 1 0  0  2  2  0 0 0 0 | * * * * 6 * * *
... 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  0  2  0  2 0 1 0 | * * * * * 6 * *
.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 3 0 2 | * * * * * * 2 *
... .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 3 2 | * * * * * * * 2
or
o.. o.. o..3o..    & | 6 *  2  4 2 0 0 | 1  2  2  8 3  8 |  4  4 4  4  4 12 | 2 2  6  6
.o. .o. .o.3.o.      | * 4  0  6 0 1 1 | 0  6  6  6 0  6 |  6  6 2  6  6  6 | 2 2  6  6
---------------------+-----+------------+-----------------+------------------+----------
... ... x.. ...    & | 2 0 | 6  * * * *  1  0  0  4 1  0 |  2  2 4  0  0  4 | 2 2  2  2
oo. oo. oo.3oo.&#x & | 1 1 | * 24 * * *  0  1  1  2 0  2 |  2  2 1  2  2  3 | 1 1  3  3
o.o o.o o.o3o.o&#x   | 2 0 | *  * 6 * *  0  0  0  0 2  4 |  0  0 0  2  2  8 | 0 0  4  4
.x. ... ... ...      | 0 2 | *  * * 2 *  0  6  0  0 0  0 |  6  0 0  6  0  0 | 2 0  6  0
... .x. ... ...      | 0 2 | *  * * * 2  0  0  6  0 0  0 |  0  6 0  0  6  0 | 0 2  0  6
---------------------+-----+------------+-----------------+------------------+----------
... ... x..3o..    & | 3 0 | 3  0 0 0 0 | 2  *  *  * *  * |  0  0 4  0  0  0 | 2 2  0  0
ox. ... ... ...&#x & | 1 2 | 0  2 0 1 0 | * 12  *  * *  * |  2  0 0  2  0  0 | 1 0  3  0
... ox. ... ...&#x & | 1 2 | 0  2 0 0 1 | *  * 12  * *  * |  0  2 0  0  2  0 | 0 1  0  3
... ... xo. ...&#x & | 2 1 | 1  2 0 0 0 | *  *  * 24 *  * |  1  1 1  0  0  1 | 1 1  1  1
... ... x.o ...&#x & | 3 0 | 1  0 2 0 0 | *  *  *  * 6  * |  0  0 0  0  0  4 | 0 0  2  2
ooo ooo ooo3ooo&#x   | 2 1 | 0  2 1 0 0 | *  *  *  * * 24 |  0  0 0  1  1  2 | 0 0  2  2
---------------------+-----+------------+-----------------+------------------+----------
ox. ... xo. ...&#x &  2 2 | 1  4 0 1 0 | 0  2  0  2 0  0 | 12  * *  *  *  * | 1 0  1  0
... ox. xo. ...&#x &  2 2 | 1  4 0 0 1 | 0  0  2  2 0  0 |  * 12 *  *  *  * | 0 1  0  1
... ... xo.3oo.&#x &  3 1 | 3  3 0 0 0 | 1  0  0  3 0  0 |  *  * 8  *  *  * | 1 1  0  0
oxo ... ... ...&#x    2 2 | 0  4 1 1 0 | 0  2  0  0 0  2 |  *  * * 12  *  * | 0 0  2  0
... oxo ... ...&#x    2 2 | 0  4 1 0 1 | 0  0  2  0 0  2 |  *  * *  * 12  * | 0 0  0  2
... ... xoo ...&#x &  3 1 | 1  3 2 0 0 | 0  0  0  1 1  2 |  *  * *  *  * 24 | 0 0  1  1
---------------------+-----+------------+-----------------+------------------+----------
ox. ... xo.3oo.&#x &  3 2 | 3  6 0 1 0 | 1  3  0  6 0  0 |  3  0 2  0  0  0 | 4 *  *  *
... ox. xo.3oo.&#x &  3 2 | 3  6 0 0 1 | 1  0  3  6 0  0 |  0  3 2  0  0  0 | * 4  *  *
oxo ... xoo ...&#x &  3 2 | 1  6 2 1 0 | 0  3  0  2 1  4 |  1  0 0  2  0  2 | * * 12  *
... oxo xoo ...&#x &  3 2 | 1  6 2 0 1 | 0  0  3  2 1  4 |  0  1 0  0  2  2 | * *  * 12

xoo3ooo3oox oqo&#xt   → both heights = 1/sqrt(8) = 0.353553
(tet || pseudo perp q-line || dual tet)

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

oxoo3oooo3ooox&#xr   → all cyclical heights = sqrt(5/8) = 0.790569
                       in fact a rhomb with diagonals 
                       height(1,3) = sqrt(2) = 1.414214
                       height(2,4) = 1/sqrt(2) = 0.707107

o...3o...3o...    | 1 * * *  4 4 0 0  0 0 0 | 6 6 12 0 0  0  0  0 0 0 | 4 4 12 12 0 0 0 0 0  0  0 0 0 | 1 1 4 6 4 0 0 0 0 0
.o..3.o..3.o..    | * 4 * *  1 0 3 1  3 0 0 | 3 0  3 3 3  6  3  3 0 0 | 3 0  6  3 1 3 3 3 1  6  3 0 0 | 1 0 3 3 1 1 3 3 1 0
..o.3..o.3..o.    | * * 1 *  0 0 0 4  0 4 0 | 0 0  0 0 6  0  0 12 6 0 | 0 0  0  0 0 4 0 0 0 12 12 4 0 | 0 0 0 0 0 1 4 6 4 1
...o3...o3...o    | * * * 4  0 1 0 0  3 1 3 | 0 3  3 0 0  3  6  3 3 3 | 0 3  3  6 0 0 1 3 3  3  6 3 1 | 0 1 1 3 3 0 1 3 3 1
------------------+---------+----------------+-------------------------+-------------------------------+--------------------
oo..3oo..3oo..&#x | 1 1 0 0 | 4 * * *  * * *  3 0  3 0 0  0  0  0 0 0 | 3 0  6  3 0 0 0 0 0  0  0 0 0 | 1 0 3 3 1 0 0 0 0 0
o..o3o..o3o..o&#x | 1 0 0 1 | * 4 * *  * * *  0 3  3 0 0  0  0  0 0 0 | 0 3  3  6 0 0 0 0 0  0  0 0 0 | 0 1 1 3 3 0 0 0 0 0
.x.. .... ....    | 0 2 0 0 | * * 6 *  * * *  1 0  0 2 1  2  0  0 0 0 | 2 0  2  0 1 2 2 1 0  2  0 0 0 | 1 0 2 1 0 1 2 1 0 0
.oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * 4  * * *  0 0  0 0 3  0  0  3 0 0 | 0 0  0  0 0 3 0 0 0  6  3 0 0 | 0 0 0 0 0 1 3 3 1 0
.o.o3.o.o3.o.o&#x | 0 1 0 1 | * * * * 12 * *  0 0  1 0 0  2  2  1 0 0 | 0 0  2  2 0 0 1 2 1  2  2 0 0 | 0 0 1 2 1 0 1 2 1 0
..oo3..oo3..oo&#x | 0 0 1 1 | * * * *  * 4 *  0 0  0 0 0  0  0  3 3 0 | 0 0  0  0 0 0 0 0 0  3  6 3 0 | 0 0 0 0 0 0 1 3 3 1
.... .... ...x    | 0 0 0 2 | * * * *  * * 6  0 1  0 0 0  0  2  0 1 2 | 0 2  0  2 0 0 0 1 2  0  2 2 1 | 0 1 0 1 2 0 0 1 2 1
------------------+---------+----------------+-------------------------+-------------------------------+--------------------
ox.. .... ....&#x | 1 2 0 0 | 2 0 1 0  0 0 0 | 6 *  * * *  *  *  * * * | 2 0  2  0 0 0 0 0 0  0  0 0 0 | 1 0 2 1 0 0 0 0 0 0
.... .... o..x&#x | 1 0 0 2 | 0 2 0 0  0 0 1 | * 6  * * *  *  *  * * * | 0 2  0  2 0 0 0 0 0  0  0 0 0 | 0 1 0 1 2 0 0 0 0 0
oo.o3oo.o3oo.o&#x | 1 1 0 1 | 1 1 0 0  1 0 0 | * * 12 * *  *  *  * * * | 0 0  2  2 0 0 0 0 0  0  0 0 0 | 0 0 1 2 1 0 0 0 0 0
.x..3.o.. ....    | 0 3 0 0 | 0 0 3 0  0 0 0 | * *  * 4 *  *  *  * * * | 1 0  0  0 1 1 1 0 0  0  0 0 0 | 1 0 1 0 0 1 1 0 0 0
.xo. .... ....&#x | 0 2 1 0 | 0 0 1 2  0 0 0 | * *  * * 6  *  *  * * * | 0 0  0  0 0 2 0 0 0  2  0 0 0 | 0 0 0 0 0 1 2 1 0 0
.x.o .... ....&#x | 0 2 0 1 | 0 0 1 0  2 0 0 | * *  * * * 12  *  * * * | 0 0  1  0 0 0 1 1 0  1  0 0 0 | 0 0 1 1 0 0 1 1 0 0
.... .... .o.x&#x | 0 1 0 2 | 0 0 0 0  2 0 1 | * *  * * *  * 12  * * * | 0 0  0  1 0 0 0 1 1  0  1 0 0 | 0 0 0 1 1 0 0 1 1 0
.ooo3.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 1  1 1 0 | * *  * * *  *  * 12 * * | 0 0  0  0 0 0 0 0 0  2  2 0 0 | 0 0 0 0 0 0 1 2 1 0
.... .... ..ox&#x | 0 0 1 2 | 0 0 0 0  0 2 1 | * *  * * *  *  *  * 6 * | 0 0  0  0 0 0 0 0 0  0  2 2 0 | 0 0 0 0 0 0 0 1 2 1
.... ...o3...x    | 0 0 0 3 | 0 0 0 0  0 0 3 | * *  * * *  *  *  * * 4 | 0 1  0  0 0 0 0 0 1  0  0 1 1 | 0 1 0 0 1 0 0 0 1 1
------------------+---------+----------------+-------------------------+-------------------------------+--------------------
ox..3oo.. ....&#x  1 3 0 0 | 3 0 3 0  0 0 0 | 3 0  0 1 0  0  0  0 0 0 | 4 *  *  * * * * * *  *  * * * | 1 0 1 0 0 0 0 0 0 0
.... o..o3o..x&#x  1 0 0 3 | 0 3 0 0  0 0 3 | 0 3  0 0 0  0  0  0 0 1 | * 4  *  * * * * * *  *  * * * | 0 1 0 0 1 0 0 0 0 0
ox.o .... ....&#x  1 2 0 1 | 2 1 1 0  2 0 0 | 1 0  2 0 0  1  0  0 0 0 | * * 12  * * * * * *  *  * * * | 0 0 1 1 0 0 0 0 0 0
.... .... oo.x&#x  1 1 0 2 | 1 2 0 0  2 0 1 | 0 1  2 0 0  0  1  0 0 0 | * *  * 12 * * * * *  *  * * * | 0 0 0 1 1 0 0 0 0 0
.x..3.o..3.o..     0 4 0 0 | 0 0 6 0  0 0 0 | 0 0  0 4 0  0  0  0 0 0 | * *  *  * 1 * * * *  *  * * * | 1 0 0 0 0 1 0 0 0 0
.xo.3.oo. ....&#x  0 3 1 0 | 0 0 3 3  0 0 0 | 0 0  0 1 3  0  0  0 0 0 | * *  *  * * 4 * * *  *  * * * | 0 0 0 0 0 1 1 0 0 0
.x.o3.o.o ....&#x  0 3 0 1 | 0 0 3 0  3 0 0 | 0 0  0 1 0  3  0  0 0 0 | * *  *  * * * 4 * *  *  * * * | 0 0 1 0 0 0 1 0 0 0
.x.o .... .o.x&#x  0 2 0 2 | 0 0 1 0  4 0 1 | 0 0  0 0 0  2  2  0 0 0 | * *  *  * * * * 6 *  *  * * * | 0 0 0 1 0 0 0 1 0 0
.... .o.o3.o.x&#x  0 1 0 3 | 0 0 0 0  3 0 3 | 0 0  0 0 0  0  3  0 0 1 | * *  *  * * * * * 4  *  * * * | 0 0 0 0 1 0 0 0 1 0
.xoo .... ....&#x  0 2 1 1 | 0 0 1 2  2 1 0 | 0 0  0 0 1  1  0  2 0 0 | * *  *  * * * * * * 12  * * * | 0 0 0 0 0 0 1 1 0 0
.... .... .oox&#x  0 1 1 2 | 0 0 0 1  2 2 1 | 0 0  0 0 0  0  1  2 1 0 | * *  *  * * * * * *  * 12 * * | 0 0 0 0 0 0 0 1 1 0
.... ..oo3..ox&#x  0 0 1 3 | 0 0 0 0  0 3 3 | 0 0  0 0 0  0  0  0 3 1 | * *  *  * * * * * *  *  * 4 * | 0 0 0 0 0 0 0 0 1 1
...o3...o3...x     0 0 0 4 | 0 0 0 0  0 0 6 | 0 0  0 0 0  0  0  0 0 4 | * *  *  * * * * * *  *  * * 1 | 0 1 0 0 0 0 0 0 0 1
------------------+---------+----------------+-------------------------+-------------------------------+--------------------
ox..3oo..3oo..&#x  1 4 0 0 | 4 0 6 0  0 0 0 | 6 0  0 4 0  0  0  0 0 0 | 4 0  0  0 1 0 0 0 0  0  0 0 0 | 1 * * * * * * * * *
o..o3o..o3o..x&#x  1 0 0 4 | 0 4 0 0  0 0 6 | 0 6  0 0 0  0  0  0 0 4 | 0 4  0  0 0 0 0 0 0  0  0 0 1 | * 1 * * * * * * * *
ox.o3oo.o ....&#x  1 3 0 1 | 3 1 3 0  3 0 0 | 3 0  3 1 0  3  0  0 0 0 | 1 0  3  0 0 0 1 0 0  0  0 0 0 | * * 4 * * * * * * *
ox.o .... oo.x&#x  1 2 0 2 | 2 2 1 0  4 0 1 | 1 1  4 0 0  2  2  0 0 0 | 0 0  2  2 0 0 0 1 0  0  0 0 0 | * * * 6 * * * * * *
.... oo.o3oo.x&#x  1 1 0 3 | 1 3 0 0  3 0 3 | 0 3  3 0 0  0  3  0 0 1 | 0 1  0  3 0 0 0 0 1  0  0 0 0 | * * * * 4 * * * * *
.xo.3.oo.3.oo.&#x  0 4 1 0 | 0 0 6 4  0 0 0 | 0 0  0 4 6  0  0  0 0 0 | 0 0  0  0 1 4 0 0 0  0  0 0 0 | * * * * * 1 * * * *
.xoo3.ooo ....&#x  0 3 1 1 | 0 0 3 3  3 1 0 | 0 0  0 1 3  3  0  3 0 0 | 0 0  0  0 0 1 1 0 0  3  0 0 0 | * * * * * * 4 * * *
.xoo .... .oox&#x  0 2 1 2 | 0 0 1 2  4 2 1 | 0 0  0 0 1  2  2  4 1 0 | 0 0  0  0 0 0 0 1 0  2  2 0 0 | * * * * * * * 6 * *
.... .ooo3.oox&#x  0 1 1 3 | 0 0 0 1  3 3 3 | 0 0  0 0 0  0  3  3 3 1 | 0 0  0  0 0 0 0 0 1  0  3 1 0 | * * * * * * * * 4 *
..oo3..oo3..ox&#x  0 0 1 4 | 0 0 0 0  0 4 6 | 0 0  0 0 0  0  0  0 6 4 | 0 0  0  0 0 0 0 0 0  0  0 4 1 | * * * * * * * * * 1
or
o...3o...3o...    & | 2 *   8  0  0 | 12 12 0  0 |  8 0 24 0 0 | 2  8  6
.o..3.o..3.o..    & | * 8   2  3  3 |  6  6 3  9 |  6 1 18 4 3 | 2  8  6
--------------------+-----+----------+------------+-------------+--------
oo..3oo..3oo..&#x & | 1 1 | 16  *  *   3  3 0  0 |  3 0  9 0 0 | 1  4  3
.x.. .... ....    & | 0 2 |  * 12  *   2  0 2  2 |  4 1  4 2 1 | 2  4  2
.o.o3.o.o3.o.o&#x   | 0 2 |  *  * 12   0  2 0  4 |  0 0  8 2 2 | 0  4  4
--------------------+-----+----------+------------+-------------+--------
ox.. .... ....&#x & | 1 2 |  2  1  0 | 24  * *  * |  2 0  2 0 0 | 1  2  1
oo.o3oo.o3oo.o&#x & | 1 2 |  2  0  1 |  * 24 *  * |  0 0  4 0 0 | 0  2  2
.x..3.o.. ....    & | 0 3 |  0  3  0 |  *  * 8  * |  2 1  0 1 0 | 2  2  0
.x.o .... ....&#x & | 0 3 |  0  1  2 |  *  * * 24 |  0 0  2 1 1 | 0  2  2
--------------------+-----+----------+------------+-------------+--------
ox..3oo.. ....&#x &  1 3 |  3  3  0 |  3  0 1  0 | 16 *  * * * | 1  1  0
.x..3.o..3.o..    &  0 4 |  0  6  0 |  0  0 4  0 |  * 2  * * * | 2  0  0
ox.o .... ....&#x &  1 3 |  3  1  2 |  1  2 0  1 |  * * 48 * * | 0  1  1
.x.o3.o.o ....&#x &  0 4 |  0  3  3 |  0  0 1  3 |  * *  * 8 * | 0  2  0
.x.o .... .o.x&#x    0 4 |  0  2  4 |  0  0 0  4 |  * *  * * 6 | 0  0  2
--------------------+-----+----------+------------+-------------+--------
ox..3oo..3oo..&#x &  1 4 |  4  6  0 |  6  0 4  0 |  4 1  0 0 0 | 4  *  *
ox.o3oo.o ....&#x &  1 4 |  4  3  3 |  3  3 1  3 |  1 0  3 1 0 | * 16  *
ox.o .... oo.x&#x &  1 4 |  4  2  4 |  2  4 0  4 |  0 0  4 0 1 | *  * 12

o(xo)o3o(oo)o3o(ox)o&#xt   → both heights = 1/sqrt(2) = 0.707107
(pt || (tet || dual tet) || pt)

o(..).3o(..).3o(..).     & | 2 *  4 4  0  0 |  6  6 12 0  0 | 4 4 12 12 0 0 0 | 1 1 4  6 4
.(o.).3.(o.).3.(o.).     & | * 8  1 1  3  3 |  3  3  6 3  9 | 3 3  9  9 1 4 3 | 1 1 4  6 4
---------------------------+-----+-----------+---------------+-----------------+-----------
o(o.).3o(o.).3o(o.).&#x  & | 1 1 | 8 *  *  *   3  0  3 0  0 | 3 0  6  3 0 0 0 | 1 0 3  3 1
o(.o).3o(.o).3o(.o).&#x  & | 1 1 | * 8  *  *   0  3  3 0  0 | 0 3  3  6 0 0 0 | 0 1 1  3 3
.(x.). .(..). .(..).     & | 0 2 | * * 12  *   1  1  0 2  2 | 2 2  2  2 1 2 1 | 1 1 2  2 2
.(oo).3.(oo).3.(oo).&#x    | 0 2 | * *  * 12   0  0  2 0  4 | 0 0  4  4 0 2 2 | 0 0 2  4 2
---------------------------+-----+-----------+---------------+-----------------+-----------
o(x.). .(..). .(..).&#x  & | 1 2 | 2 0  1  0 | 12  *  * *  * | 2 0  2  0 0 0 0 | 1 0 2  1 0
.(..). .(..). o(.x).&#x  & | 1 2 | 0 2  1  0 |  * 12  * *  * | 0 2  0  2 0 0 0 | 0 1 0  1 2
o(oo).3o(oo).3o(oo).&#x  & | 1 2 | 1 1  0  1 |  *  * 24 *  * | 0 0  2  2 0 0 0 | 0 0 1  2 1
.(x.).3.(o.). .(..).     & | 0 3 | 0 0  3  0 |  *  *  * 8  * | 1 1  0  0 1 1 0 | 1 1 1  0 1
.(xo). .(..). .(..).&#x  & | 0 3 | 0 0  1  2 |  *  *  * * 24 | 0 0  1  1 0 1 1 | 0 0 1  2 1
---------------------------+-----+-----------+---------------+-----------------+-----------
o(x.).3o(o.). .(..).&#x  &  1 3 | 3 0  3  0 |  3  0  0 1  0 | 8 *  *  * * * * | 1 0 1  0 0
.(..). o(.o).3o(.x).&#x  &  1 3 | 0 3  3  0 |  0  3  0 1  0 | * 8  *  * * * * | 0 1 0  0 1
o(xo). .(..). .(..).&#x  &  1 3 | 2 1  1  2 |  1  0  2 0  1 | * * 24  * * * * | 0 0 1  1 0
.(..). .(..). o(ox).&#x  &  1 3 | 1 2  1  2 |  0  1  2 0  1 | * *  * 24 * * * | 0 0 0  1 1
.(x.).3.(o.).3.(o.).     &  0 4 | 0 0  6  0 |  0  0  0 4  0 | * *  *  * 2 * * | 1 1 0  0 0
.(xo).3.(oo). .(..).&#x  &  0 4 | 0 0  3  3 |  0  0  0 1  3 | * *  *  * * 8 * | 0 0 1  0 1
.(xo). .(..). .(ox).&#x     0 4 | 0 0  2  4 |  0  0  0 0  4 | * *  *  * * * 6 | 0 0 0  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 | 2 * *  * *
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 | * 2 *  * *
o(xo).3o(oo). .(..).&#x  &  1 4 | 3 1  3  3 |  3  0  3 1  3 | 1 0  3  0 0 1 0 | * * 8  * *
o(xo). .(..). o(ox).&#x  &  1 4 | 2 2  2  4 |  1  1  4 0  4 | 0 0  2  2 0 0 1 | * * * 12 *
.(..). o(oo).3o(ox).&#x  &  1 4 | 1 3  3  3 |  0  3  3 1  3 | 0 1  0  3 0 1 0 | * * *  * 8

xoxo oxoo3ooox&#xr   → all cyclical heights = sqrt(5/12) = 0.645497
                       in fact a rhomb with diagonals 
                       height(1,3) = 1
                       height(2,4) = sqrt(2/3) = 0.816497

o... o...3o...    | 2 * * *  1 3 1 3 0 0 0 0 0 0 | 3 3 3 3 3  6 3 0 0 0 0 0  0 0 0 0 | 3 1 3 1 3 6 3 3 3  6 0 0 0 0 0 0 0 | 1 1 1 3 3 1 3 3 0 0 0 0
.o.. .o..3.o..    | * 3 * *  0 2 0 0 2 2 2 0 0 0 | 1 4 0 0 2  4 0 1 1 4 2 1  4 0 0 0 | 2 2 0 0 4 2 4 2 0  4 2 2 2 4 2 0 0 | 1 0 2 2 1 0 4 2 1 2 1 0
..o. ..o.3..o.    | * * 2 *  0 0 1 0 0 3 0 1 3 0 | 0 0 0 0 3  0 3 0 3 3 0 0  6 3 3 0 | 0 0 0 0 3 0 0 0 3  6 3 1 6 3 3 3 1 | 0 0 1 0 0 1 3 3 1 3 3 1
...o ...o3...o    | * * * 3  0 0 0 2 0 0 2 0 2 2 | 0 0 1 4 0  4 2 0 0 0 1 2  4 1 4 1 | 0 0 2 2 0 2 2 4 4  4 0 0 2 2 4 2 2 | 0 1 0 1 2 2 2 4 0 1 2 1
------------------+---------+---------------------+-----------------------------------+------------------------------------+------------------------
x... .... ....    | 2 0 0 0 | 1 * * * * * * * * *  3 0 3 0 0  0 0 0 0 0 0 0  0 0 0 0 | 3 0 3 0 0 6 0 0 0  0 0 0 0 0 0 0 0 | 1 1 0 3 3 0 0 0 0 0 0 0
oo.. oo..3oo..&#x | 1 1 0 0 | * 6 * * * * * * * *  1 2 0 0 1  2 0 0 0 0 0 0  0 0 0 0 | 2 1 0 0 2 2 2 1 0  2 0 0 0 0 0 0 0 | 1 0 1 2 1 0 2 1 0 0 0 0
o.o. o.o.3o.o.&#x | 1 0 1 0 | * * 2 * * * * * * *  0 0 0 0 3  0 3 0 0 0 0 0  0 0 0 0 | 0 0 0 0 3 0 0 0 3  6 0 0 0 0 0 0 0 | 0 0 1 0 0 1 3 3 0 0 0 0
o..o o..o3o..o&#x | 1 0 0 1 | * * * 6 * * * * * *  0 0 1 2 0  2 1 0 0 0 0 0  0 0 0 0 | 0 0 2 1 0 2 1 2 2  2 0 0 0 0 0 0 0 | 0 1 0 1 2 1 1 2 0 0 0 0
.... .x.. ....    | 0 2 0 0 | * * * * 3 * * * * *  0 2 0 0 0  0 0 1 0 2 1 0  0 0 0 0 | 1 2 0 0 2 0 2 0 0  0 1 2 0 2 0 0 0 | 1 0 2 1 0 0 2 0 1 1 0 0
.oo. .oo.3.oo.&#x | 0 1 1 0 | * * * * * 6 * * * *  0 0 0 0 1  0 0 0 1 2 0 0  2 0 0 0 | 0 0 0 0 2 0 0 0 0  2 2 1 2 2 1 0 0 | 0 0 1 0 0 0 2 1 1 2 1 0
.o.o .o.o3.o.o&#x | 0 1 0 1 | * * * * * * 6 * * *  0 0 0 0 0  2 0 0 0 0 1 1  2 0 0 0 | 0 0 0 0 0 1 2 2 0  2 0 0 1 2 2 0 0 | 0 0 0 1 1 0 2 2 0 1 1 0
..x. .... ....    | 0 0 2 0 | * * * * * * * 1 * *  0 0 0 0 0  0 0 0 3 0 0 0  0 3 0 0 | 0 0 0 0 0 0 0 0 0  0 3 0 6 0 0 3 0 | 0 0 0 0 0 0 0 0 1 3 3 1
..oo ..oo3..oo&#x | 0 0 1 1 | * * * * * * * * 6 *  0 0 0 0 0  0 1 0 0 0 0 0  2 1 2 0 | 0 0 0 0 0 0 0 0 2  2 0 0 2 1 2 2 1 | 0 0 0 0 0 1 1 2 0 1 2 1
.... .... ...x    | 0 0 0 2 | * * * * * * * * * 3  0 0 0 2 0  0 0 0 0 0 0 1  0 0 2 1 | 0 0 1 2 0 0 0 2 2  0 0 0 0 0 2 1 2 | 0 1 0 0 1 2 0 2 0 0 1 1
------------------+---------+---------------------+-----------------------------------+------------------------------------+------------------------
xo.. .... ....&#x | 2 1 0 0 | 1 2 0 0 0 0 0 0 0 0 | 3 * * * *  * * * * * * *  * * * * | 2 0 0 0 0 2 0 0 0  0 0 0 0 0 0 0 0 | 1 0 0 2 1 0 0 0 0 0 0 0
.... ox.. ....&#x | 1 2 0 0 | 0 2 0 0 1 0 0 0 0 0 | * 6 * * *  * * * * * * *  * * * * | 1 1 0 0 1 0 1 0 0  0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 1 0 0 0 0 0
x..o .... ....&#x | 2 0 0 1 | 1 0 0 2 0 0 0 0 0 0 | * * 3 * *  * * * * * * *  * * * * | 0 0 2 0 0 2 0 0 0  0 0 0 0 0 0 0 0 | 0 1 0 1 2 0 0 0 0 0 0 0
.... .... o..x&#x | 1 0 0 2 | 0 0 0 2 0 0 0 0 0 1 | * * * 6 *  * * * * * * *  * * * * | 0 0 1 1 0 0 0 1 1  0 0 0 0 0 0 0 0 | 0 1 0 0 1 1 0 1 0 0 0 0
ooo. ooo.3ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 0 | * * * * 6  * * * * * * *  * * * * | 0 0 0 0 2 0 0 0 0  2 0 0 0 0 0 0 0 | 0 0 1 0 0 0 2 1 0 0 0 0
oo.o oo.o3oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 1 0 0 0 | * * * * * 12 * * * * * *  * * * * | 0 0 0 0 0 1 1 1 0  1 0 0 0 0 0 0 0 | 0 0 0 1 1 0 1 1 0 0 0 0
o.oo o.oo3o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 1 0 | * * * * *  * 6 * * * * *  * * * * | 0 0 0 0 0 0 0 0 2  2 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 2 0 0 0 0
.... .x..3.o..    | 0 3 0 0 | 0 0 0 0 3 0 0 0 0 0 | * * * * *  * * 1 * * * *  * * * * | 0 2 0 0 0 0 0 0 0  0 0 2 0 0 0 0 0 | 1 0 2 0 0 0 0 0 1 0 0 0
.ox. .... ....&#x | 0 1 2 0 | 0 0 0 0 0 2 0 1 0 0 | * * * * *  * * * 3 * * *  * * * * | 0 0 0 0 0 0 0 0 0  0 2 0 2 0 0 0 0 | 0 0 0 0 0 0 0 0 1 2 1 0
.... .xo. ....&#x | 0 2 1 0 | 0 0 0 0 1 2 0 0 0 0 | * * * * *  * * * * 6 * *  * * * * | 0 0 0 0 1 0 0 0 0  0 1 1 0 1 0 0 0 | 0 0 1 0 0 0 1 0 1 1 0 0
.... .x.o ....&#x | 0 2 0 1 | 0 0 0 0 1 0 2 0 0 0 | * * * * *  * * * * * 3 *  * * * * | 0 0 0 0 0 0 2 0 0  0 0 0 0 2 0 0 0 | 0 0 0 1 0 0 2 0 0 1 0 0
.... .... .o.x&#x | 0 1 0 2 | 0 0 0 0 0 0 2 0 0 1 | * * * * *  * * * * * * 3  * * * * | 0 0 0 0 0 0 0 2 0  0 0 0 0 0 2 0 0 | 0 0 0 0 1 0 0 2 0 0 1 0
.ooo .ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 0 1 1 0 1 0 | * * * * *  * * * * * * * 12 * * * | 0 0 0 0 0 0 0 0 0  1 0 0 1 1 1 0 0 | 0 0 0 0 0 0 1 1 0 1 1 0
..xo .... ....&#x | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 | * * * * *  * * * * * * *  * 3 * * | 0 0 0 0 0 0 0 0 0  0 0 0 2 0 0 2 0 | 0 0 0 0 0 0 0 0 0 1 2 1
.... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 2 1 | * * * * *  * * * * * * *  * * 6 * | 0 0 0 0 0 0 0 0 1  0 0 0 0 0 1 1 1 | 0 0 0 0 0 1 0 1 0 0 1 1
.... ...o3...x    | 0 0 0 3 | 0 0 0 0 0 0 0 0 0 3 | * * * * *  * * * * * * *  * * * 1 | 0 0 0 2 0 0 0 0 0  0 0 0 0 0 0 0 2 | 0 1 0 0 0 2 0 0 0 0 0 1
------------------+---------+---------------------+-----------------------------------+------------------------------------+------------------------
xo.. ox.. ....&#x  2 2 0 0 | 1 4 0 0 1 0 0 0 0 0 | 2 2 0 0 0  0 0 0 0 0 0 0  0 0 0 0 | 3 * * * * * * * *  * * * * * * * * | 1 0 0 1 0 0 0 0 0 0 0 0
.... ox..3oo..&#x  1 3 0 0 | 0 3 0 0 3 0 0 0 0 0 | 0 3 0 0 0  0 0 1 0 0 0 0  0 0 0 0 | * 2 * * * * * * *  * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 0 0
x..o .... o..x&#x  2 0 0 2 | 1 0 0 4 0 0 0 0 0 1 | 0 0 2 2 0  0 0 0 0 0 0 0  0 0 0 0 | * * 3 * * * * * *  * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 0 0
.... o..o3o..x&#x  1 0 0 3 | 0 0 0 3 0 0 0 0 0 3 | 0 0 0 3 0  0 0 0 0 0 0 0  0 0 0 1 | * * * 2 * * * * *  * * * * * * * * | 0 1 0 0 0 1 0 0 0 0 0 0
.... oxo. ....&#x  1 2 1 0 | 0 2 1 0 1 2 0 0 0 0 | 0 1 0 0 2  0 0 0 0 1 0 0  0 0 0 0 | * * * * 6 * * * *  * * * * * * * * | 0 0 1 0 0 0 1 0 0 0 0 0
xo.o .... ....&#x  2 1 0 1 | 1 2 0 2 0 0 1 0 0 0 | 1 0 1 0 0  2 0 0 0 0 0 0  0 0 0 0 | * * * * * 6 * * *  * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 0
.... ox.o ....&#x  1 2 0 1 | 0 2 0 1 1 0 2 0 0 0 | 0 1 0 0 0  2 0 0 0 0 1 0  0 0 0 0 | * * * * * * 6 * *  * * * * * * * * | 0 0 0 1 0 0 1 0 0 0 0 0
.... .... oo.x&#x  1 1 0 2 | 0 1 0 2 0 0 2 0 0 1 | 0 0 0 1 0  2 0 0 0 0 0 1  0 0 0 0 | * * * * * * * 6 *  * * * * * * * * | 0 0 0 0 1 0 0 1 0 0 0 0
.... .... o.ox&#x  1 0 1 2 | 0 0 1 2 0 0 0 0 2 1 | 0 0 0 1 0  0 2 0 0 0 0 0  0 0 1 0 | * * * * * * * * 6  * * * * * * * * | 0 0 0 0 0 1 0 1 0 0 0 0
oooo oooo3oooo&#x  1 1 1 1 | 0 1 1 1 0 1 1 0 1 0 | 0 0 0 0 1  1 1 0 0 0 0 0  1 0 0 0 | * * * * * * * * * 12 * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 0
.ox. .xo. ....&#x  0 2 2 0 | 0 0 0 0 1 4 0 1 0 0 | 0 0 0 0 0  0 0 0 2 2 0 0  0 0 0 0 | * * * * * * * * *  * 3 * * * * * * | 0 0 0 0 0 0 0 0 1 1 0 0
.... .xo.3.oo.&#x  0 3 1 0 | 0 0 0 0 3 3 0 0 0 0 | 0 0 0 0 0  0 0 1 0 3 0 0  0 0 0 0 | * * * * * * * * *  * * 2 * * * * * | 0 0 1 0 0 0 0 0 1 0 0 0
.oxo .... ....&#x  0 1 2 1 | 0 0 0 0 0 2 1 1 2 0 | 0 0 0 0 0  0 0 0 1 0 0 0  2 1 0 0 | * * * * * * * * *  * * * 6 * * * * | 0 0 0 0 0 0 0 0 0 1 1 0
.... .xoo ....&#x  0 2 1 1 | 0 0 0 0 1 2 2 0 1 0 | 0 0 0 0 0  0 0 0 0 1 1 0  2 0 0 0 | * * * * * * * * *  * * * * 6 * * * | 0 0 0 0 0 0 1 0 0 1 0 0
.... .... .oox&#x  0 1 1 2 | 0 0 0 0 0 1 2 0 2 1 | 0 0 0 0 0  0 0 0 0 0 0 1  2 0 1 0 | * * * * * * * * *  * * * * * 6 * * | 0 0 0 0 0 0 0 1 0 0 1 0
..xo .... ..ox&#x  0 0 2 2 | 0 0 0 0 0 0 0 1 4 1 | 0 0 0 0 0  0 0 0 0 0 0 0  0 2 2 0 | * * * * * * * * *  * * * * * * 3 * | 0 0 0 0 0 0 0 0 0 0 1 1
.... ..oo3..ox&#x  0 0 1 3 | 0 0 0 0 0 0 0 0 3 3 | 0 0 0 0 0  0 0 0 0 0 0 0  0 0 3 1 | * * * * * * * * *  * * * * * * * 2 | 0 0 0 0 0 1 0 0 0 0 0 1
------------------+---------+---------------------+-----------------------------------+------------------------------------+------------------------
xo.. ox..3oo..&#x  2 3 0 0 | 1 6 0 0 3 0 0 0 0 0 | 3 6 0 0 0  0 0 1 0 0 0 0  0 0 0 0 | 3 2 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * *
x..o o..o3o..x&#x  2 0 0 3 | 1 0 0 6 0 0 0 0 0 3 | 0 0 3 6 0  0 0 0 0 0 0 0  0 0 0 1 | 0 0 3 2 0 0 0 0 0  0 0 0 0 0 0 0 0 | * 1 * * * * * * * * * *
.... oxo.3ooo.&#x  1 3 1 0 | 0 3 1 0 3 3 0 0 0 0 | 0 3 0 0 3  0 0 1 0 3 0 0  0 0 0 0 | 0 1 0 0 3 0 0 0 0  0 0 1 0 0 0 0 0 | * * 2 * * * * * * * * *
xo.o ox.o ....&#x  2 2 0 1 | 1 4 0 2 1 0 2 0 0 0 | 2 2 1 0 0  4 0 0 0 0 1 0  0 0 0 0 | 1 0 0 0 0 2 2 0 0  0 0 0 0 0 0 0 0 | * * * 3 * * * * * * * *
xo.o .... oo.x&#x  2 1 0 2 | 1 2 0 4 0 0 2 0 0 1 | 1 0 2 2 0  4 0 0 0 0 0 1  0 0 0 0 | 0 0 1 0 0 2 0 2 0  0 0 0 0 0 0 0 0 | * * * * 3 * * * * * * *
.... o.oo3o.ox&#x  1 0 1 3 | 0 0 1 3 0 0 0 0 3 3 | 0 0 0 3 0  0 3 0 0 0 0 0  0 0 3 1 | 0 0 0 1 0 0 0 0 3  0 0 0 0 0 0 0 1 | * * * * * 2 * * * * * *
.... oxoo ....&#x  1 2 1 1 | 0 2 1 1 1 2 2 0 1 0 | 0 1 0 0 2  2 1 0 0 1 1 0  2 0 0 0 | 0 0 0 0 1 0 1 0 0  2 0 0 0 1 0 0 0 | * * * * * * 6 * * * * *
.... .... ooox&#x  1 1 1 2 | 0 1 1 2 0 1 2 0 2 1 | 0 0 0 1 1  2 2 0 0 0 0 1  2 0 1 0 | 0 0 0 0 0 0 0 1 1  2 0 0 0 0 1 0 0 | * * * * * * * 6 * * * *
.ox. .xo.3.oo.&#x  0 3 2 0 | 0 0 0 0 3 6 0 1 0 0 | 0 0 0 0 0  0 0 1 3 6 0 0  0 0 0 0 | 0 0 0 0 0 0 0 0 0  0 3 2 0 0 0 0 0 | * * * * * * * * 1 * * *
.oxo .xoo ....&#x  0 2 2 1 | 0 0 0 0 1 4 2 1 2 0 | 0 0 0 0 0  0 0 0 2 2 1 0  4 1 0 0 | 0 0 0 0 0 0 0 0 0  0 1 0 2 2 0 0 0 | * * * * * * * * * 3 * *
.oxo .... .oox&#x  0 1 2 2 | 0 0 0 0 0 2 2 1 4 1 | 0 0 0 0 0  0 0 0 1 0 0 1  4 2 2 0 | 0 0 0 0 0 0 0 0 0  0 0 0 2 0 2 1 0 | * * * * * * * * * * 3 *
..xo ..oo3..ox&#x  0 0 2 3 | 0 0 0 0 0 0 0 1 6 3 | 0 0 0 0 0  0 0 0 0 0 0 0  0 3 6 1 | 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 3 2 | * * * * * * * * * * * 1

xo4oo ox3oo4oo&#zx   → height = 0
(tegum sum of {4} and perp oct)
(tegum product of {4} with oct)

o.4o. o.3o.4o.    | 4 *  2  6  0 | 12 12 0 | 24  8 | 16
.o4.o .o3.o4.o    | * 6  0  4  4 |  4 16 4 | 16 16 | 16
------------------+-----+---------+---------+-------+---
x. .. .. .. ..    | 2 0 | 4  *  *   6  0 0 | 12  0 |  8
oo4oo oo3oo4oo&#x | 1 1 | * 24  *   2  4 0 |  8  4 |  8
.. .. .x .. ..    | 0 2 | *  * 12   0  4 2 |  4  8 |  8
------------------+-----+---------+---------+-------+---
xo .. .. .. ..&#x | 2 1 | 1  2  0 | 24  * * |  4  0 |  4
.. .. ox .. ..&#x | 1 2 | 0  2  1 |  * 48 * |  2  2 |  4
.. .. .x3.o ..    | 0 3 | 0  0  3 |  *  * 8 |  0  4 |  4
------------------+-----+---------+---------+-------+---
xo .. ox .. ..&#x  2 2 | 1  4  1 |  2  2 0 | 48  * |  2
.. .. ox3oo ..&#x  1 3 | 0  3  3 |  0  3 1 |  * 32 |  2
------------------+-----+---------+---------+-------+---
xo .. ox3oo ..&#x  2 3 | 1  6  3 |  3  6 1 |  3  2 | 32

xo xo oo3ox3oo&#zx   → height = 0
(tegum sum of {4} and perp oct)
(tegum product of {4} with oct)

o. o. o.3o.3o.    | 4 *  1 1  6  0 |  6  6 12 0 0 | 12 12  4  4 | 4 4 4 4
.o .o .o3.o3.o    | * 6  0 0  4  4 |  2  2 16 2 2 |  8  8  8  8 | 4 4 4 4
------------------+-----+-----------+--------------+-------------+--------
x. .. .. .. ..    | 2 0 | 2 *  *  *   6  0  0 0 0 | 12  0  0  0 | 4 4 0 0
.. x. .. .. ..    | 2 0 | * 2  *  *   0  6  0 0 0 |  0 12  0  0 | 0 0 4 4
oo oo oo3oo3oo&#x | 1 1 | * * 24  *   1  1  4 0 0 |  4  4  2  2 | 2 2 2 2
.. .. .. .x ..    | 0 2 | * *  * 12   0  0  4 1 1 |  2  2  4  4 | 2 2 2 2
------------------+-----+-----------+--------------+-------------+--------
xo .. .. .. ..&#x | 2 1 | 1 0  2  0 | 12  *  * * * |  4  0  0  0 | 2 2 0 0
.. xo .. .. ..&#x | 2 1 | 0 1  2  0 |  * 12  * * * |  0  4  0  0 | 0 0 2 2
.. .. .. ox ..&#x | 1 2 | 0 0  2  1 |  *  * 48 * * |  1  1  1  1 | 1 1 1 1
.. .. .o3.x ..    | 0 3 | 0 0  0  3 |  *  *  * 4 * |  0  0  4  0 | 2 0 2 0
.. .. .. .x3.o    | 0 3 | 0 0  0  3 |  *  *  * * 4 |  0  0  0  4 | 0 2 0 2
------------------+-----+-----------+--------------+-------------+--------
xo .. .. ox ..&#x  2 2 | 1 0  4  1 |  2  0  2 0 0 | 24  *  *  * | 1 1 0 0
.. xo .. ox ..&#x  2 2 | 0 1  4  1 |  0  2  2 0 0 |  * 24  *  * | 0 0 1 1
.. .. oo3ox ..&#x  1 3 | 0 0  3  3 |  0  0  3 1 0 |  *  * 16  * | 1 0 1 0
.. .. .. ox3oo&#x  1 3 | 0 0  3  3 |  0  0  3 0 1 |  *  *  * 16 | 0 1 0 1
------------------+-----+-----------+--------------+-------------+--------
xo .. oo3ox ..&#x  2 3 | 1 0  6  3 |  3  0  6 1 0 |  3  0  2  0 | 8 * * *
xo .. .. ox3oo&#x  2 3 | 1 0  6  3 |  3  0  6 0 1 |  3  0  0  2 | * 8 * *
.. xo oo3ox ..&#x  2 3 | 0 1  6  3 |  0  3  6 1 0 |  0  3  2  0 | * * 8 *
.. xo .. ox3oo&#x  2 3 | 0 1  6  3 |  0  3  6 0 1 |  0  3  0  2 | * * * 8

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