Acronym rag (old: ric)
Name rectified hexacontitetrapeton,
lattice B6 contact polytope (span of its small roots),
lattice D6 contact polytope (span of its roots)
Circumradius 1
Lace city
in approx. ASCII-art
 ©  
o   h   o	-- x3o3o3o4o (tac)
         
h   I   h	-- o3x3o3o4o (rat)
         
o   h   o	-- x3o3o3o4o (tac)

   \   \   \   \   \
     \   \   \   \   +-- o o3o3o4o (point)
       \   \   \   +---- x x3o3o4o (hexip)
         \   \   +------ compound of:
           \   \         o o3x3o4o (ico)
             \   \       u o3o3o4o (u-line)
               \   +---- x x3o3o4o (hexip)
                 +------ o o3o3o4o (point)

where:
o = o3o3o *b3o (point)
h = x3o3o *b3o (hex)
I = o3x3o *b3o (ico)
  p   P  	-- x3o3o3o4o (tac)
         
         
r   S   R	-- o3x3o3o4o (rat)
         
         
  p   P  	-- x3o3o3o4o (tac)

    \   \   \
     \   \   +- o3x3o3o3o (rix)
      \   +---- x3o3o3o3x (scad)
       +------- o3o3o3x3o (inv. rix)

where:
p = x3o3o3o (pen)
P = o3o3o3x (dual pen)
r = o3x3o3o (rap)
R = o3o3x3o (inv. rap)
S = x3o3o3x (spid)
Lace hyper city
in approx. ASCII-art
    o    
         
o   O   o
         
    o    
o   O   o
         
O   C   O
         
o   O   o
    o    
         
o   O   o
         
    o    
where:
o = o3o4o (point)
O = x3o4o (oct)
C = o3x4o (co)
Coordinates (1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0)   & all permutations, all changes of sign
Dihedral angles
(at margins)
  • at rap between rix and rix:   arccos(-2/3) = 131.810315°
  • at pen between rix and tac:   arccos[-1/sqrt(6)] = 114.094843°
Confer
related segmentopeta:
taccarat   rixascad   hexipaico   hexippy   squahex  
related scaliform:
xedrag  
related CRFs:
raddirag  
External
links
wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

o3x3o3o3o4o

. . . . . . | 60   16 |   8  48 |  24  64 |  32  32 | 16  2
------------+----+-----+---------+---------+---------+------
. x . . . . |  2 | 480 |   1   6 |   6  12 |  12   8 |  8  1
------------+----+-----+---------+---------+---------+------
o3x . . . . |  3 |   3 | 160   *    6   0 |  12   0 |  8  0
. x3o . . . |  3 |   3 |   * 960 |   1   4 |   4   4 |  4  1
------------+----+-----+---------+---------+---------+------
o3x3o . . .   6 |  12 |   4   4 | 240   * |   4   0 |  4  0
. x3o3o . .   4 |   6 |   0   4 |   * 960 |   1   2 |  2  1
------------+----+-----+---------+---------+---------+------
o3x3o3o . .  10 |  30 |  10  20 |   5   5 | 192   * |  2  0
. x3o3o3o .   5 |  10 |   0  10 |   0   5 |   * 384 |  1  1
------------+----+-----+---------+---------+---------+------
o3x3o3o3o .  15 |  60 |  20  60 |  15  30 |   6   6 | 64  *
. x3o3o3o4o  10 |  40 |   0  80 |   0  80 |   0  32 |  * 12

o3x3o3o3o4/3o

. . . . .   . | 60   16 |   8  48 |  24  64 |  32  32 | 16  2
--------------+----+-----+---------+---------+---------+------
. x . . .   . |  2 | 480 |   1   6 |   6  12 |  12   8 |  8  1
--------------+----+-----+---------+---------+---------+------
o3x . . .   . |  3 |   3 | 160   *    6   0 |  12   0 |  8  0
. x3o . .   . |  3 |   3 |   * 960 |   1   4 |   4   4 |  4  1
--------------+----+-----+---------+---------+---------+------
o3x3o . .   .   6 |  12 |   4   4 | 240   * |   4   0 |  4  0
. x3o3o .   .   4 |   6 |   0   4 |   * 960 |   1   2 |  2  1
--------------+----+-----+---------+---------+---------+------
o3x3o3o .   .  10 |  30 |  10  20 |   5   5 | 192   * |  2  0
. x3o3o3o   .   5 |  10 |   0  10 |   0   5 |   * 384 |  1  1
--------------+----+-----+---------+---------+---------+------
o3x3o3o3o   .  15 |  60 |  20  60 |  15  30 |   6   6 | 64  *
. x3o3o3o4/3o  10 |  40 |   0  80 |   0  80 |   0  32 |  * 12

o3o3o *b3o3x3o

. . .    . . . | 60   16 |  48   8 |  64  24 |  16  16  32 |  2  8  8
---------------+----+-----+---------+---------+-------------+---------
. . .    . x . |  2 | 480 |   6   1 |  12   6 |   4   4  12 |  1  4  4
---------------+----+-----+---------+---------+-------------+---------
. . .    o3x . |  3 |   3 | 960   * |   4   1 |   2   2   4 |  1  2  2
. . .    . x3o |  3 |   3 |   * 160    0   6 |   0   0  12 |  0  4  4
---------------+----+-----+---------+---------+-------------+---------
. o . *b3o3x .   4 |   6 |   4   0 | 960   * |   1   1   1 |  1  1  1
. . .    o3x3o   6 |  12 |   4   4 |   * 240 |   0   0   4 |  0  2  2
---------------+----+-----+---------+---------+-------------+---------
o3o . *b3o3x .   5 |  10 |  10   0 |   5   0 | 192   *   * |  1  1  0
. o3o *b3o3x .   5 |  10 |  10   0 |   5   0 |   * 192   * |  1  0  1
. o . *b3o3x3o  10 |  30 |  20  10 |   5   5 |   *   * 192 |  0  1  1
---------------+----+-----+---------+---------+-------------+---------
o3o3o *b3o3x .  10 |  40 |  80   0 |  80   0 |  16  16   0 | 12  *  *
o3o . *b3o3x3o  15 |  60 |  60  20 |  30  15 |   6   0   6 |  * 32  *
. o3o *b3o3x3o  15 |  60 |  60  20 |  30  15 |   0   6   6 |  *  * 32

xox3oxo3ooo3ooo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(tac || (pseudo) rat || tac)

o..3o..3o..3o..4o..    & | 20  *   8   8   0 |  24  8  24  0   0 |  32  24  32  0   0 | 16  32  16  0 | 1 16  1
.o.3.o.3.o.3.o.4.o.      |  * 40   0   4  12 |   0  2  24  6  24 |   0  12  48 12  16 |  0  24  32  8 | 0 16  2
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x.. ... ... ... ...    & |  2  0 | 80   *   * |   6  1   0  0   0 |  12   6   0  0   0 |  8  12   0  0 | 1  8  0
oo.3oo.3oo.3oo.4oo.&#x & |  1  1 |  * 160   * |   0  1   6  0   0 |   0   6  12  0   0 |  0  12   8  0 | 0  8  1
... .x. ... ... ...      |  0  2 |  *   * 240 |   0  0   2  1   4 |   0   2   8  4   4 |  0   8   8  4 | 0  8  1
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x..3o.. ... ... ...    & |  3  0 |  3   0   0 | 160  *   *  *   * |   4   1   0  0   0 |  4   4   0  0 | 1  4  0
xo. ... ... ... ...&#x & |  2  1 |  1   2   0 |   * 80   *  *   *    0   6   0  0   0 |  0  12   0  0 | 0  8  0
... ox. ... ... ...&#x & |  1  2 |  0   2   1 |   *  * 480  *   * |   0   1   4  0   0 |  0   4   4  0 | 0  4  1
.o.3.x. ... ... ...      |  0  3 |  0   0   3 |   *  *   * 80   *    0   2   0  4   0 |  0   8   0  4 | 0  8  0
... .x.3.o. ... ...      |  0  3 |  0   0   3 |   *  *   *  * 320 |   0   0   2  1   2 |  0   2   4  2 | 0  4  1
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x..3o..3o.. ... ...    &   4  0 |  6   0   0 |   4  0   0  0   0 | 160   *   *  *   * |  2   1   0  0 | 1  2  0
xo.3ox. ... ... ...&#x &   3  3 |  3   6   3 |   1  3   3  1   0 |   * 160   *  *   * |  0   4   0  0 | 0  4  0
... ox.3oo. ... ...&#x &   1  3 |  0   3   3 |   0  0   3  0   1 |   *   * 640  *   * |  0   1   2  0 | 0  2  1
.o.3.x.3.o. ... ...        0  6 |  0   0  12 |   0  0   0  4   4 |   *   *   * 80   * |  0   2   0  2 | 0  4  0
... .x.3.o.3.o. ...        0  4 |  0   0   6 |   0  0   0  0   4 |   *   *   *  * 160 |  0   0   2  1 | 0  2  1
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x..3o..3o..3o.. ...    &   5  0 | 10   0   0 |  10  0   0  0   0 |   5   0   0  0   0 | 64   *   *  * | 1  1  0
xo.3ox.3oo. ... ...&#x &   4  6 |  6  12  12 |   4  6  12  4   4 |   1   4   4  1   0 |  * 160   *  * | 0  2  0
... ox.3oo.3oo. ...&#x &   1  4 |  0   4   6 |   0  0   6  0   4 |   0   0   4  0   1 |  *   * 320  * | 0  1  1
.o.3.x.3.o.3.o. ...        0 10 |  0   0  30 |   0  0   0 10  20 |   0   0   0  5   5 |  *   *   * 32 | 0  2  0
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x..3o..3o..3o..4o..    &  10  0 | 40   0   0 |  80  0   0  0   0 |  80   0   0  0   0 | 32   0   0  0 | 2  *  *
xo.3ox.3oo.3oo. ...&#x &   5 10 | 10  20  30 |  10 10  30 10  20 |   5  10  20  5   5 |  1   5   5  1 | * 64  *
... oxo3ooo3ooo4ooo&#xt    2  8 |  0  16  24 |   0  0  48  0  32 |   0   0  64  0  16 |  0   0  32  0 | *  * 10

oq ox3xo3oo3oo4oo&#zx   → height = 0
(tegum sum of rat with a q-laced taccup variant)

o. o.3o.3o.3o.4o.     | 40  *   12   4  0 |  6  24  2  24   0 | 12  16  12  48   0 |  8  24  32  0 |  2 16 0
.o .o3.o3.o3.o4.o     |  * 20    0   8  8 |  0   0  8  24  24 |  0   0  24  32  32 |  0  32  16 16 |  1 16 1
----------------------+-------+------------+-------------------+--------------------+---------------+--------
.. .. x. .. .. ..     |  2  0 | 240   *  * |  1   4  0   2   0 |  4   4   2   8   0 |  4   8   8  0 |  1  8 0
oo oo3oo3oo3oo4oo&#x  |  1  1 |   * 160  * |  0   0  1   6   0 |  0   0   6  12   0 |  0  12   8  0 |  1  8 0
.. .x .. .. .. ..     |  0  2 |   *   * 80 |  0   0  1   0   6 |  0   0   6   0  12 |  0  12   0  8 |  0  8 1
----------------------+-------+------------+-------------------+--------------------+---------------+--------
.. o.3x. .. .. ..     |  3  0 |   3   0  0 | 80   *  *   *   *   4   0   2   0   0 |  4   8   0  0 |  0  8 0
.. .. x.3o. .. ..     |  3  0 |   3   0  0 |  * 320  *   *   * |  1   2   0   2   0 |  2   2   4  0 |  1  4 0
.. ox .. .. .. ..&#x  |  1  2 |   0   2  1 |  *   * 80   *   *   0   0   6   0   0 |  0  12   0  0 |  0  8 0
.. .. xo .. .. ..&#x  |  2  1 |   1   2  0 |  *   *  * 480   * |  0   0   1   4   0 |  0   4   4  0 |  1  4 0
.. .x3.o .. .. ..     |  0  3 |   0   0  3 |  *   *  *   * 160 |  0   0   1   0   4 |  0   4   0  4 |  0  4 1
----------------------+-------+------------+-------------------+--------------------+---------------+--------
.. o.3x.3o. .. ..       6  0 |  12   0  0 |  4   4  0   0   0 | 80   *   *   *   * |  2   2   0  0 |  0  4 0
.. .. x.3o.3o. ..       4  0 |   6   0  0 |  0   4  0   0   0 |  * 160   *   *   * |  1   0   2  0 |  1  2 0
.. ox3xo .. .. ..&#x    3  3 |   3   6  3 |  1   0  3   3   1 |  *   * 160   *   * |  0   4   0  0 |  0  4 0
.. .. xo3oo .. ..&#x    3  1 |   3   3  0 |  0   1  0   3   0 |  *   *   * 640   * |  0   1   2  0 |  1  2 0
.. .x3.o3.o .. ..       0  4 |   0   0  6 |  0   0  0   0   4 |  *   *   *   * 160 |  0   1   0  2 |  0  2 1
----------------------+-------+------------+-------------------+--------------------+---------------+--------
.. o.3x.3o.3o. ..      10  0 |  30   0  0 | 10  20  0   0   0 |  5   5   0   0   0 | 32   *   *  * |  0  2 0
.. ox3xo3oo .. ..&#x    6  4 |  12  12  6 |  4   4  6  12   4 |  1   0   4   4   1 |  * 160   *  * |  0  2 0
.. .. xo3oo3oo ..&#x    4  1 |   6   4  0 |  0   4  0   6   0 |  0   1   0   4   0 |  *   * 320  * |  1  1 0
.. .x3.o3.o3.o ..       0  5 |   0   0 10 |  0   0  0   0  10 |  0   0   0   0   5 |  *   *   * 64 |  0  1 1
----------------------+-------+------------+-------------------+--------------------+---------------+--------
oq .. xo3oo3oo4oo&#zx   8  2 |  24  16  0 |  0  32  0  48   0 |  0  16   0  64   0 |  0   0  32  0 | 10  * *
.. ox3xo3oo3oo ..&#x   10  5 |  30  20 10 | 10  20 10  30  10 |  5   5  10  20   5 |  1   5   5  1 |  * 64 *
.. .x3.o3.o3.o4.o       0 10 |   0   0 40 |  0   0  0   0  80 |  0   0   0   0  80 |  0   0   0 32 |  *  * 2

oxo3xoo3ooo3oox3oxo&#xt   → both heights = 1/sqrt(3) = 0.577350
(rix || pseudo scad || inv rix)

o..3o..3o..3o..3o..     & | 30  *    8   8   0 |  4  12   4  12  24   0 |  6  8  12  24  24   8  6  0 |  4  2 12  8  12   8  2  16  0 | 1  4  2  7  4
.o.3.o.3.o.3.o.3.o.       |  * 30    0   8   8 |  0   0   8  24  12  12 |  0  0  12   8  24  24 12  8 |  0  0  8  2   8  12  8  24  2 | 0  2  2  8  6
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
... x.. ... ... ...     & |  2  0 | 120   *   * |  1   3   0   0   3   0 |  3  3   3   6   3   0  0  0 |  3  1  6  3   3   1  0   3  0 | 1  3  1  3  1
oo.3oo.3oo.3oo.3oo.&#x  & |  1  1 |   * 240   * |  0   0   1   3   3   0 |  0  0   3   3   6   3  3  0 |  0  0  3  1   3   3  1   9  0 | 0  1  1  4  3
.x. ... ... ... ...     & |  0  2 |   *   * 120 |  0   0   1   3   0   3 |  0  0   3   0   3   6  3  3 |  0  0  3  0   1   3  3   9  1 | 0  1  1  4  3
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
o..3x.. ... ... ...     & |  3  0 |   3   0   0 | 40   *   *   *   *   *   3  0   3   0   0   0  0  0 |  3  0  6  0   0   0  0   3  0 | 1  3  0  3  1
... x..3o.. ... ...     & |  3  0 |   3   0   0 |  * 120   *   *   *   * |  1  2   0   2   0   0  0  0 |  2  1  2  2   1   0  0   0  0 | 1  2  1  1  0
ox. ... ... ... ...&#x  & |  1  2 |   0   2   1 |  *   * 120   *   *   *   0  0   3   0   0   0  3  0 |  0  0  3  0   0   0  0   9  0 | 0  1  0  4  3
... ... ... ... ox.&#x  & |  1  2 |   0   2   1 |  *   *   * 360   *   * |  0  0   0   0   2   2  1  0 |  0  0  0  0   1   2  1   4  0 | 0  0  1  2  2
... xo. ... ... ...&#x  & |  2  1 |   1   2   0 |  *   *   *   * 360   * |  0  0   1   2   2   0  0  0 |  0  0  2  1   2   1  0   2  0 | 0  1  1  2  1
.x.3.o. ... ... ...     & |  0  3 |   0   0   3 |  *   *   *   *   * 120 |  0  0   1   0   0   2  0  2 |  0  0  2  0   0   1  2   2  1 | 0  1  1  2  1
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
o..3x..3o.. ... ...     &   6  0 |  12   0   0 |  4   4   0   0   0   0 | 30  *   *   *   *   *  *  * |  2  0  2  0   0   0  0   0  0 | 1  2  0  1  0
... x..3o..3o.. ...     &   4  0 |   6   0   0 |  0   4   0   0   0   0 |  * 60   *   *   *   *  *  * |  1  1  0  1   0   0  0   0  0 | 1  1  1  0  0
ox.3xo. ... ... ...&#x  &   3  3 |   3   6   3 |  1   0   3   0   3   1 |  *  * 120   *   *   *  *  * |  0  0  2  0   0   0  0   2  0 | 0  1  0  2  1
... xo.3oo. ... ...&#x  &   3  1 |   3   3   0 |  0   1   0   0   3   0 |  *  *   * 240   *   *  *  * |  0  0  1  1   1   0  0   0  0 | 0  1  1  1  0
... xo. ... ... ox.&#x  &   2  2 |   1   4   1 |  0   0   0   2   2   0 |  *  *   *   * 360   *  *  * |  0  0  0  0   1   1  0   1  0 | 0  0  1  1  1
... ... ... oo.3ox.&#x  &   1  3 |   0   3   3 |  0   0   0   3   0   1 |  *  *   *   *   * 240  *  * |  0  0  0  0   0   1  1   1  0 | 0  0  1  1  1
oxo ... ... ... oxo&#xt     2  4 |   0   8   4 |  0   0   4   4   0   0 |  *  *   *   *   *   * 90  * |  0  0  0  0   0   0  0   4  0 | 0  0  0  2  2
.x.3.o.3.o. ... ...     &   0  4 |   0   0   6 |  0   0   0   0   0   4 |  *  *   *   *   *   *  * 60 |  0  0  1  0   0   0  1   0  1 | 0  1  1  1  0
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
o..3x..3o..3o.. ...     &  10  0 |  30   0   0 | 10  20   0   0   0   0 |  5  5   0   0   0   0  0  0 | 12  *  *  *   *   *  *   *  * | 1  1  0  0  0
... x..3o..3o..3o..     &   5  0 |  10   0   0 |  0  10   0   0   0   0 |  0  5   0   0   0   0  0  0 |  * 12  *  *   *   *  *   *  * | 1  0  1  0  0
ox.3xo.3oo. ... ...&#x  &   6  4 |  12  12   6 |  4   4   6   0  12   4 |  1  0   4   4   0   0  0  1 |  *  * 60  *   *   *  *   *  * | 0  1  0  1  0
... xo.3oo.3oo. ...&#x  &   4  1 |   6   4   0 |  0   4   0   0   6   0 |  0  1   0   4   0   0  0  0 |  *  *  * 60   *   *  *   *  * | 0  1  1  0  0
... xo.3oo. ... ox.&#x  &   3  2 |   3   6   1 |  0   1   0   3   6   0 |  0  0   0   2   3   0  0  0 |  *  *  *  * 120   *  *   *  * | 0  0  1  1  0
... xo. ... oo.3ox.&#x  &   2  3 |   1   6   3 |  0   0   0   6   3   1 |  0  0   0   0   3   2  0  0 |  *  *  *  *   * 120  *   *  * | 0  0  1  0  1
... ... oo.3oo.3ox.&#x  &   1  4 |   0   4   6 |  0   0   0   6   0   4 |  0  0   0   0   0   4  0  1 |  *  *  *  *   *   * 60   *  * | 0  0  1  1  0
oxo3xoo ... ... oxo&#xt &   4  6 |   3  18   9 |  1   0   9  12   6   2 |  0  0   2   0   3   2  3  0 |  *  *  *  *   *   *  * 120  * | 0  0  0  1  1
.x.3.o.3.o.3.o. ...     &   0  5 |   0   0  10 |  0   0   0   0   0  10 |  0  0   0   0   0   0  0  5 |  *  *  *  *   *   *  *   * 12 | 0  1  1  0  0
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
o..3x..3o..3o..3o..     &  15  0 |  60   0   0 | 20  60   0   0   0   0 | 15 30   0   0   0   0  0  0 |  6  6  0  0   0   0  0   0  0 | 2  *  *  *  *
ox.3xo.3oo.3oo. ...&#x  &  10  5 |  30  20  10 | 10  20  10   0  30  10 |  5  5  10  20   0   0  0  5 |  1  0  5  5   0   0  0   0  1 | * 12  *  *  *
... xo.3oo.3oo.3ox.&#x  &   5  5 |  10  20  10 |  0  10   0  30  30  10 |  0  5   0  20  30  20  0  5 |  0  1  0  5  10  10  5   0  1 | *  * 12  *  *
oxo3xoo3ooo ... oxo&#xt &   7  8 |  12  32  16 |  4   4  16  24  24   8 |  1  0   8   8  12   8  6  2 |  0  0  2  0   4   0  2   4  0 | *  *  * 30  *
oxo3xoo ... oox3oxo&#xt     6  9 |   6  36  18 |  2   0  18  36  18   6 |  0  0   6   0  18  12  9  0 |  0  0  0  0   0   6  0   6  0 | *  *  *  * 20

oxo4ooq oxo3xoo3ooo4ooo&#zx   → height = 0
(tegum sum of ico, squahex and perp-gyro q-{4})

o..4o.. o..3o..3o..4o..     | 24  * *   8   8  0  0  0 |  4  8   8  4  32   0  0   0 |  4  4  32  16  32  0   0 |  16  32 16   0 | 2 16 0
.o.4.o. .o.3.o.3.o.4.o.     |  * 32 *   0   6  2  6  2 |  0  0  12  6  12  12  2  12 |  0 12  24  12   8  8  24 |  24  16  8  16 | 1 16 1
..o4..o ..o3..o3..o4..o     |  *  * 4   0   0  0  0 16 |  0  0   0  0   0   0  8  48 |  0 24   0   0   0  0  64 |  32   0  0  32 | 0 16 2
----------------------------+---------+-----------------+-----------------------------+--------------------------+----------------+-------
... ... ... x.. ... ...     |  2  0 0 | 96   *  *  *  * |  1  2   0  0   4   0  0   0 |  2  0   4   4   8  0   0 |   4   8  8   0 | 1  8 0
oo.4oo. oo.3oo.3oo.4oo.&#x  |  1  1 0 |  * 192  *  *  * |  0  0   2  1   4   0  0   0 |  0  2   8   4   4  0   0 |   8   8  4   0 | 1  8 0
.x. ... ... ... ... ...     |  0  2 0 |  *   * 32  *  * |  0  0   6  0   0   0  1   0 |  0  6  12   0   0  0   0 |  12   8  0   0 | 1  8 0
... ... .x. ... ... ...     |  0  2 0 |  *   *  * 96  * |  0  0   0  1   0   4  0   2 |  0  2   0   4   0  4   8 |   8   0  4   8 | 0  8 1
.oo4.oo .oo3.oo3.oo4.oo&#x  |  0  1 1 |  *   *  *  * 64 |  0  0   0  0   0   0  1   6 |  0  6   0   0   0  0  12 |  12   0  0   8 | 0  8 1
----------------------------+---------+-----------------+-----------------------------+--------------------------+----------------+-------
... ... o..3x.. ... ...     |  3  0 0 |  3   0  0  0  0 | 32  *   *  *   *   *  *   *   2  0   0   4   0  0   0 |   4   0  8   0 | 0  8 0
... ... ... x..3o.. ...     |  3  0 0 |  3   0  0  0  0 |  * 64   *  *   *   *  *   * |  1  0   0   0   4  0   0 |   0   4  4   0 | 1  4 0
ox. ... ... ... ... ...&#x  |  1  2 0 |  0   2  1  0  0 |  *  * 192  *   *   *  *   * |  0  1   4   0   0  0   0 |   4   4  0   0 | 1  4 0
... ... ox. ... ... ...&#x  |  1  2 0 |  0   2  0  1  0 |  *  *   * 96   *   *  *   *   0  2   0   4   0  0   0 |   8   0  4   0 | 0  8 0
... ... ... xo. ... ...&#x  |  2  1 0 |  1   2  0  0  0 |  *  *   *  * 384   *  *   * |  0  0   2   1   2  0   0 |   2   4  2   0 | 1  4 0
... ... .x.3.o. ... ...     |  0  3 0 |  0   0  0  3  0 |  *  *   *  *   * 128  *   * |  0  0   0   1   0  2   2 |   2   0  2   4 | 0  4 1
.xo ... ... ... ... ...&#x  |  0  2 1 |  0   0  1  0  2 |  *  *   *  *   *   * 32   *   0  6   0   0   0  0   0 |  12   0  0   0 | 0  8 0
... ... .xo ... ... ...&#x  |  0  2 1 |  0   0  0  1  2 |  *  *   *  *   *   *  * 192 |  0  1   0   0   0  0   4 |   4   0  0   4 | 0  4 1
----------------------------+---------+-----------------+-----------------------------+--------------------------+----------------+-------
... ... o..3x..3o.. ...       6  0 0 | 12   0  0  0  0 |  4  4   0  0   0   0  0   0 | 16  *   *   *   *  *   * |   0   0  4   0 | 0  4 0
oxo ... oxo ... ... ...&#xt   1  4 1 |  0   4  2  2  4 |  0  0   2  2   0   0  2   2 |  * 96   *   *   *  *   * |   4   0  0   0 | 0  4 0
ox. ... ... xo. ... ...&#x    2  2 0 |  1   4  1  0  0 |  0  0   2  0   2   0  0   0 |  *  * 384   *   *  *   * |   1   2  0   0 | 1  2 0
... ... ox.3xo. ... ...&#x    3  3 0 |  3   6  0  3  0 |  1  0   0  3   3   1  0   0 |  *  *   * 128   *  *   * |   2   0  2   0 | 0  4 0
... ... ... xo.3oo. ...&#x    3  1 0 |  3   3  0  0  0 |  0  1   0  0   3   0  0   0 |  *  *   *   * 256  *   * |   0   2  1   0 | 1  2 0
... ... .x.3.o.3.o. ...       0  4 0 |  0   0  0  6  0 |  0  0   0  0   0   4  0   0 |  *  *   *   *   * 64   * |   0   0  1   2 | 0  2 1
... ... .xo3.oo ... ...&#x    0  3 1 |  0   0  0  3  3 |  0  0   0  0   0   1  0   3 |  *  *   *   *   *  * 256 |   1   0  0   2 | 0  2 1
----------------------------+---------+-----------------+-----------------------------+--------------------------+----------------+-------
oxo ... oxo3xoo ... ...&#xt   3  6 1 |  3  12  3  6  6 |  1  0   6  6   6   2  3   6 |  0  3   3   2   0  0   2 | 128   *  *   * | 0  2 0
ox. ... ... xo.3oo. ...&#x    3  2 0 |  3   6  1  0  0 |  0  1   3  0   6   0  0   0 |  0  0   3   0   2  0   0 |   * 256  *   * | 1  1 0
... ... ox.3xo.3oo. ...&#x    6  4 0 | 12  12  0  6  0 |  4  4   0  6  12   4  0   0 |  1  0   0   4   4  1   0 |   *   * 64   * | 0  2 0
... ... .xo3.oo3.oo ...&#x    0  4 1 |  0   0  0  6  4 |  0  0   0  0   0   4  0   6 |  0  0   0   0   0  1   4 |   *   *  * 128 | 0  1 1
----------------------------+---------+-----------------+-----------------------------+--------------------------+----------------+-------
ox.4oo. ... xo.3oo.4oo.&#zx   6  4 0 | 12  24  4  0  0 |  0  8  24  0  48   0  0   0 |  0  0  48   0  32  0   0 |   0  32  0   0 | 8  * *
oxo ... oxo3xoo3ooo ...&#xt   6  8 1 | 12  24  4 12  8 |  4  4  12 12  24   8  4  12 |  1  6  12   8   8  2   8 |   4   4  2   2 | * 64 *
... .oq .xo3.oo3.oo4.oo&#x    0  8 2 |  0   0  0 24 16 |  0  0   0  0   0  32  0  48 |  0  0   0   0   0 16  64 |   0   0  0  32 | *  * 4

oxo3oox4ooo oxo3xoo4ooo&#zx   → all existing heights = 0
(tegum sum of 2 mutually perp coes with octdip)

o..3o..4o.. o..3o..4o..     | 12  *  *   4  12  0  0   0  0 | 2  24  6  24  0  0  0   0   0 0 |  16  12  48 12  0   0   0 |  8  32 24   0 | 2 16 0
.o.3.o.4.o. .o.3.o.4.o.     |  * 36  *   0   4  4  4   4  0 | 0  16  4   4  4  4  4   4  16 0 |  16  16  16  4  4  16  16 | 16  16 16  16 | 1 16 1
..o3..o4..o ..o3..o4..o     |  *  * 12   0   0  0  0  12  4 | 0   0  0   0  0  0  6  24  24 2 |   0  12   0  0 12  48  16 | 24   0  8  32 | 0 16 2
----------------------------+----------+---------------------+---------------------------------+---------------------------+---------------+-------
... ... ... ... x.. ...     |  2  0  0 | 24   *  *  *   *  * | 1   0  0   6  0  0  0   0   0 0 |   0   0  12  6  0   0   0 |  0   8 12   0 | 1  8 0
oo.3oo.4oo. oo.3oo.4oo.&#x  |  1  1  0 |  * 144  *  *   *  * | 0   4  1   2  0  0  0   0   0 0 |   4   4   8  2  0   0   0 |  4   8  8   0 | 1  8 0
.x. ... ... ... ... ...     |  0  2  0 |  *   * 72  *   *  * | 0   4  0   0  2  0  1   0   0 0 |   8   4   4  0  2   0   0 |  8   8  4   0 | 1  8 0
... ... ... .x. ... ...     |  0  2  0 |  *   *  * 72   *  * | 0   0  1   0  0  2  0   0   4 0 |   0   4   0  2  0   4   8 |  4   0  8   8 | 0  8 1
.oo3.oo4.oo .oo3.oo4.oo&#x  |  0  1  1 |  *   *  *  * 144  * | 0   0  0   0  0  0  1   2   4 0 |   0   4   0  0  2   8   4 |  8   0  4   8 | 0  8 1
... ..x ... ... ... ...     |  0  0  2 |  *   *  *  *   * 24 | 0   0  0   0  0  0  0   6   0 1 |   0   0   0  0  6  12   0 | 12   0  0   8 | 0  8 1
----------------------------+----------+---------------------+---------------------------------+---------------------------+---------------+-------
... ... ... o..3x.. ...     |  3  0  0 |  3   0  0  0   0  0 | 8   *  *   *  *  *  *   *   * *    0   0   0  6  0   0   0 |  0   0 12   0 | 0  8 0
ox. ... ... ... ... ...&#x  |  1  2  0 |  0   2  1  0   0  0 | * 288  *   *  *  *  *   *   * * |   2   1   2  0  0   0   0 |  2   4  2   0 | 1  4 0
... ... ... ox. ... ...&#x  |  1  2  0 |  0   2  0  1   0  0 | *   * 72   *  *  *  *   *   * *    0   4   0  2  0   0   0 |  4   0  8   0 | 0  8 0
... ... ... ... xo. ...&#x  |  2  1  0 |  1   2  0  0   0  0 | *   *  * 144  *  *  *   *   * * |   0   0   4  1  0   0   0 |  0   4  4   0 | 1  4 0
.x.3.o. ... ... ... ...     |  0  3  0 |  0   0  3  0   0  0 | *   *  *   * 48  *  *   *   * * |   4   0   0  0  1   0   0 |  4   4  0   0 | 1  4 0
... ... ... .x.3.o. ...     |  0  3  0 |  0   0  0  3   0  0 | *   *  *   *  * 48  *   *   * * |   0   0   0  1  0   0   4 |  0   0  4   4 | 0  4 1
.xo ... ... ... ... ...&#x  |  0  2  1 |  0   0  1  0   2  0 | *   *  *   *  *  * 72   *   * *    0   4   0  0  2   0   0 |  8   0  4   0 | 0  8 0
... .ox ... ... ... ...&#x  |  0  1  2 |  0   0  0  0   2  1 | *   *  *   *  *  *  * 144   * * |   0   0   0  0  1   4   0 |  4   0  0   4 | 0  4 1
... ... ... .xo ... ...&#x  |  0  2  1 |  0   0  0  1   2  0 | *   *  *   *  *  *  *   * 288 * |   0   1   0  0  0   2   2 |  2   0  2   4 | 0  4 1
..o3..x ... ... ... ...     |  0  0  3 |  0   0  0  0   0  3 | *   *  *   *  *  *  *   *   * 8    0   0   0  0  6   0   0 | 12   0  0   0 | 0  8 0
----------------------------+----------+---------------------+---------------------------------+---------------------------+---------------+-------
ox.3oo. ... ... ... ...&#x    1  3  0 |  0   3  3  0   0  0 | 0   3  0   0  1  0  0   0   0 0 | 192   *   *  *  *   *   * |  1   2  0   0 | 1  2 0
oxo ... ... oxo ... ...&#xt   1  4  1 |  0   4  2  2   4  0 | 0   2  2   0  0  0  2   0   2 0 |   * 144   *  *  *   *   * |  2   0  2   0 | 0  4 0
ox. ... ... ... xo. ...&#x    2  2  0 |  1   4  1  0   0  0 | 0   2  0   2  0  0  0   0   0 0 |   *   * 288  *  *   *   * |  0   2  1   0 | 1  2 0
... ... ... ox.3xo. ...&#x    3  3  0 |  3   6  0  3   0  0 | 1   0  3   3  0  1  0   0   0 0 |   *   *   * 48  *   *   * |  0   0  4   0 | 0  4 0
.xo3.ox ... ... ... ...&#x    0  3  3 |  0   0  3  0   6  3 | 0   0  0   0  1  0  3   3   0 1 |   *   *   *  * 48   *   * |  4   0  0   0 | 0  4 0
... .ox ... .xo ... ...&#x    0  2  2 |  0   0  0  1   4  1 | 0   0  0   0  0  0  0   2   2 0 |   *   *   *  *  * 288   * |  1   0  0   2 | 0  2 1
... ... ... .xo3.oo ...&#x    0  3  1 |  0   0  0  3   3  0 | 0   0  0   0  0  1  0   0   3 0 |   *   *   *  *  *   * 192 |  0   0  1   2 | 0  2 1
----------------------------+----------+---------------------+---------------------------------+---------------------------+---------------+-------
oxo3oox ... oxo ... ...&#xt   1  6  3 |  0   6  6  3  12  3 | 0   6  3   0  2  0  6   6   6 1 |   2   3   0  0  2   3   0 | 96   *  *   * | 0  2 0
ox.3oo. ... ... xo. ...&#x    2  3  0 |  1   6  3  0   0  0 | 0   6  0   3  1  0  0   0   0 0 |   2   0   3  0  0   0   0 |  * 192  *   * | 1  1 0
oxo ... ... oxo3xoo ...&#xt   3  6  1 |  3  12  3  6   6  0 | 1   6  6   6  0  2  3   0   6 0 |   0   3   3  2  0   0   2 |  *   * 96   * | 0  2 0
... .ox ... .xo3.oo ...&#x    0  3  2 |  0   0  0  3   6  1 | 0   0  0   0  0  1  0   3   6 0 |   0   0   0  0  0   3   2 |  *   *  * 192 | 0  1 1
----------------------------+----------+---------------------+---------------------------------+---------------------------+---------------+-------
ox.3oo.4oo. ... xo.4oo.&#zx   4  6  0 |  4  24 12  0   0  0 | 0  48  0  24  8  0  0   0   0 0 |  32   0  48  0  0   0   0 |  0  32  0   0 | 6  * *
oxo3oox ... oxo3xoo ...&#xt   3  9  3 |  3  18  9  9  18  3 | 1  18  9   9  3  3  9   9  18 1 |   6   9   9  3  3   9   6 |  3   3  3   3 | * 64 *
... .ox4.oo .xo3.oo4.oo&#zx   0  6  4 |  0   0  0 12  24  4 | 0   0  0   0  0  8  0  24  48 0 |   0   0   0  0  0  48  32 |  0   0  0  32 | *  * 6
or
o..3o..4o.. o..3o..4o..     & | 24  *   4  12   0 |  2  24   6  24  0 |  16  12  48 12 |  32  32 |  2 16
.o.3.o.4.o. .o.3.o.4.o.       |  * 36   0   8   8 |  0  32   8   8  8 |  32  16  32  8 |  32  32 |  2 16
------------------------------+-------+------------+-------------------+----------------+---------+------
... ... ... ... x.. ...     & |  2  0 | 48   *   * |  1   0   0   6  0 |   0   0  12  6 |  12   8 |  1  8
oo.3oo.4oo. oo.3oo.4oo.&#x  & |  1  1 |  * 288   * |  0   4   1   2  0 |   4   4   8  2 |  12   8 |  1  8
.x. ... ... ... ... ...     & |  0  2 |  *   * 144 |  0   4   1   0  2 |   8   4   4  2 |  12   8 |  1  8
------------------------------+-------+------------+-------------------+----------------+---------+------
... ... ... o..3x.. ...     & |  3  0 |  3   0   0 | 16   *   *   *  *    0   0   0  6 |  12   0 |  0  8
ox. ... ... ... ... ...&#x  & |  1  2 |  0   2   1 |  * 576   *   *  * |   2   1   2  0 |   4   4 |  1  4
... ... ... ox. ... ...&#x  & |  1  2 |  0   2   1 |  *   * 144   *  *    0   4   0  2 |  12   0 |  0  8
... ... ... ... xo. ...&#x  & |  2  1 |  1   2   0 |  *   *   * 288  * |   0   0   4  1 |   4   4 |  1  4
.x.3.o. ... ... ... ...     & |  0  3 |  0   0   3 |  *   *   *   * 96 |   4   0   0  1 |   4   4 |  1  4
------------------------------+-------+------------+-------------------+----------------+---------+------
ox.3oo. ... ... ... ...&#x  &   1  3 |  0   3   3 |  0   3   0   0  1 | 384   *   *  * |   1   2 |  1  2
oxo ... ... oxo ... ...&#xt     2  4 |  0   8   4 |  0   4   4   0  0 |   * 144   *  * |   4   0 |  0  4
ox. ... ... ... xo. ...&#x  &   2  2 |  1   4   1 |  0   2   0   2  0 |   *   * 576  * |   1   2 |  1  2
... ... ... ox.3xo. ...&#x  &   3  3 |  3   6   3 |  1   0   3   3  1 |   *   *   * 96 |   4   0 |  0  4
------------------------------+-------+------------+-------------------+----------------+---------+------
oxo3oox ... oxo ... ...&#xt &   4  6 |  3  18   9 |  1  12   9   6  2 |   2   3   3  2 | 192   * |  0  2
ox.3oo. ... ... xo. ...&#x  &   2  3 |  1   6   3 |  0   6   0   3  1 |   2   0   3  0 |   * 384 |  1  1
------------------------------+-------+------------+-------------------+----------------+---------+------
ox.3oo.4oo. ... xo.4oo.&#zx &   4  6 |  4  24  12 |  0  48   0  24  8 |  32   0  48  0 |   0  32 | 12  *
oxo3oox ... oxo3xoo ...&#xt     6  9 |  6  36  18 |  2  36  18  18  6 |  12   9  18  6 |   6   6 |  * 64

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