Acronym ihdlaq
Name icositetra-hexa-diminished pentacontihexapentacosiheptacontihexaexon,
hexadecachoral gyro-cuboctahedronism
Circumradius 1
Lace hyper city
in approx. ASCII-art 
            _  E _         
      _  -   /    \- _     
   O_      /       _\  O   
   \  - _/   _  -     \ \  
  | \  /  E            |\\ 
     N  /    \            N
 |    / \      \      | / |
    /|    \      \    /    
| /         \      \/|   | 
N   |         \   /  N     
 \ \         _  E_  / \ |  
  \| \ _  -       /- _ \   
   O_  \        /   _  O   
      - _\    _  -         
           E               

where:
N = x3o3o *b3o (hex)
E = o3o3x *b3o (gyro hex)
O = o3o3o *b3x (alt. gyro hex)
Face vector 96, 1152, 4632, 7488, 5244, 1416, 86
Confer
uniform relative:
laq  
related scaliform:
sadlaq  
general polytopal classes:
scaliform   gyro-cuboctahedronism  
External
links 		polytopewiki  

Incidence matrix according to Dynkin symbol

xxo xox oxx oox3ooo3oxo *e3xoo&#zx   → heights = 0
(tegum sum of 3 relatively gyro-orthogonal squahexes)

o.. o.. o.. o..3o..3o.. *e3o..     & | 96 |  2   6  16 |  1  12  16  24   72  24 |   8  24   8   48   64  24   60   96 |  1  8  12  40  20  16  48   72  40   60 |  8  12  4 12  36  28  18  12 | 2  6 10 2
-------------------------------------+----+------------+-------------------------+-------------------------------------+-----------------------------------------+------------------------------+----------
x.. ... ... ... ... ...    ...     & |  2 | 96   *   * |  1  12   8   8    0   0 |   0  20   4   12    0   0   48    0 |  0  8   6   8   0   0  36   24   0    0 |  4   2  0 12  24   8   0   0 | 1  6  6 0
... ... ... ... ... ...    x..     & |  2 |  * 288   * |  0   0   0   0    8   0 |   4   0   0    4   16   4    0    8 |  1  0   2   8   8   8   0    4   8    8 |  4   4  4  0   4   4   8   2 | 2  1  4 2
oo. oo. oo. oo.3oo.3oo. *e3oo.&#x  & |  2 |  *   * 768 |  0   0   1   2    6   3 |   0   2   1    6    6   3    6    9 |  0  1   3   6   2   3   9   15   7   12 |  3   2  1  3  12   7   5   3 | 1  3  5 1
-------------------------------------+----+------------+-------------------------+-------------------------------------+-----------------------------------------+------------------------------+----------
x.. x.. ... ... ... ...    ...     & |  4 |  4   0   0 | 24   *   *   *    *   * |   0  16   0    0    0   0    0    0 |  0  8   0   0   0   0  24    0   0    0 |  0   0  0 12  12   0   0   0 | 0  6  2 0
... ... ... ... o.. ... *e3x..     & |  3 |  3   0   0 |  * 384   *   *    *   * |   2   0   0    0    4   0    0    0 |  1  0   0   2   4   4   0    0   2    0 |  2   2  4  0   0   1   4   0 | 2  0  2 2
xx. ... ... ... ... ...    ...&#x  & |  4 |  2   0   2 |  *   * 384   *    *   * |   0   2   0    0    0   0    3    0 |  0  1   0   0   0   0   6    3   0    0 |  0   0  0  3   6   1   0   0 | 0  3  2 0
... xo. ... ... ... ...    ...&#x  & |  3 |  1   0   2 |  *   *   * 768    *   * |   0   1   1    3    0   0    3    0 |  0  1   3   3   0   0   6    6   0    0 |  3   1  0  3   9   3   0   0 | 1  3  4 0
... ... ... ... ... ox.    ...&#x  & |  3 |  0   1   2 |  *   *   *   * 2304   * |   0   0   0    1    2   1    0    2 |  0  0   1   2   1   2   0    2   2    3 |  2   1  1  0   3   2   3   1 | 1  1  3 1
ooo ooo ooo ooo3ooo3ooo *e3ooo&#x    |  3 |  0   0   3 |  *   *   *   *    * 768 |   0   0   0    0    0   0    3    6 |  0  0   0   0   0   0   3    6   3    6 |  0   0  0  1   6   3   3   2 | 0  2  3 1
-------------------------------------+----+------------+-------------------------+-------------------------------------+-----------------------------------------+------------------------------+----------
... ... ... o..3o.. ... *e3x..     & ♦  4 |  0   6   0 |  0   4   0   0    0   0 | 192   *   *    *    *   *    *    * |  1  0   0   0   2   2   0    0   0    0 |  1   1  4  0   0   0   2   0 | 2  0  1 2
xx. xo. ... ... ... ...    ...&#x  & ♦  6 |  5   0   4 |  1   0   2   2    0   0 |   * 384   *    *    *   *    *    * |  0  1   0   0   0   0   3    0   0    0 |  0   0  0  3   3   0   0   0 | 0  3  1 0
... xo. ox. ... ... ...    ...&#x  & ♦  4 |  2   0   4 |  0   0   0   4    0   0 |   *   * 192    *    *   *    *    * |  0  1   3   0   0   0   3    0   0    0 |  3   0  0  3   6   0   0   0 | 1  3  3 0
... xo. ... ... ... ox.    ...&#x  & ♦  4 |  1   1   4 |  0   0   0   2    2   0 |   *   *   * 1152    *   *    *    * |  0  0   1   2   0   0   0    2   0    0 |  2   1  0  0   3   2   0   0 | 1  1  3 0
... ... ... ... oo.3ox.    ...&#x  & ♦  4 |  0   3   3 |  0   1   0   0    3   0 |   *   *   *    * 1536   *    *    * |  0  0   0   1   1   1   0    0   1    0 |  1   1  1  0   0   1   2   0 | 1  0  2 1
... ... ... ... ... ox.    xo.&#x  & ♦  4 |  0   2   4 |  0   0   0   0    4   0 |   *   *   *    *    * 576    *    * |  0  0   1   0   0   2   0    0   0    2 |  2   0  1  0   2   0   2   1 | 1  1  2 1
xxo ... ... ... ... ...    ...&#x  & ♦  5 |  4   0   4 |  0   0   1   2    0   2 |   *   *   *    *    *   * 1152    * |  0  0   0   0   0   0   2    2   0    0 |  0   0  0  1   4   1   0   0 | 0  2  2 0
... ... ... oox ... ...    ...&#x  & ♦  4 |  0   1   3 |  0   0   0   0    2   2 |   *   *   *    *    *   *    * 2304 |  0  0   0   0   0   0   0    1   1    2 |  0   0  0  0   2   1   2   1 | 0  1  2 1
-------------------------------------+----+------------+-------------------------+-------------------------------------+-----------------------------------------+------------------------------+----------
... ... ... o..3o..3o.. *e3x..     & ♦  8 |  0  24   0 |  0  32   0   0    0   0 |  16   0   0    0    0   0    0    0 | 12  *   *   *   *   *   *    *   *    * |  0   0  4  0   0   0   0   0 | 2  0  0 2
xx. xo. ox. ... ... ...    ...&#x  & ♦  8 |  8   0   8 |  2   0   4   8    0   0 |   0   4   2    0    0   0    0    0 |  * 96   *   *   *   *   *    *   *    * |  0   0  0  3   0   0   0   0 | 0  3  0 0
... xo. ox. ... ... ox.    xo.&#zx & ♦  8 |  4   4  16 |  0   0   0  16   16   0 |   0   0   4    8    0   4    0    0 |  *  * 144   *   *   *   *    *   *    * |  2   0  0  0   2   0   0   0 | 1  1  2 0
... xo. ... ... oo.3ox.    ...&#x  & ♦  5 |  1   3   6 |  0   1   0   3    6   0 |   0   0   0    3    2   0    0    0 |  *  *   * 768   *   *   *    *   *    * |  1   1  0  0   0   1   0   0 | 1  0  2 0
... ... ... oo.3oo.3ox.    ...&#x  & ♦  5 |  0   6   4 |  0   4   0   0    6   0 |   1   0   0    0    4   0    0    0 |  *  *   *   * 384   *   *    *   *    * |  0   1  1  0   0   0   1   0 | 1  0  1 1
... ... ... ... oo.3ox. *e3xo.&#x  & ♦  8 |  0  12  12 |  0   8   0   0   24   0 |   2   0   0    0    8   6    0    0 |  *  *   *   *   * 192   *    *   *    * |  1   0  1  0   0   0   1   0 | 1  0  1 1
xxo xox ... ... ... ...    ...&#x  & ♦  8 |  6   0  12 |  1   0   4   8    0   4 |   0   2   1    0    0   0    4    0 |  *  *   *   *   *   * 576    *   *    * |  0   0  0  1   2   0   0   0 | 0  2  1 0
xxo ... ... oox ... ...    ...&#x  & ♦  6 |  2   1  10 |  0   0   1   4    4   4 |   0   0   0    2    0   0    2    2 |  *  *   *   *   *   *   * 1152   *    * |  0   0  0  0   2   1   0   0 | 0  1  2 0
... ... ... oox3ooo ...    ...&#x  & ♦  5 |  0   3   7 |  0   1   0   0    6   3 |   0   0   0    0    2   0    0    3 |  *  *   *   *   *   *   *    * 768    * |  0   0  0  0   0   1   2   0 | 0  0  2 1
... ... ... oox ... oxo    ...&#x  & ♦  5 |  0   2   8 |  0   0   0   0    6   4 |   0   0   0    0    0   1    0    4 |  *  *   *   *   *   *   *    *   * 1152 |  0   0  0  0   1   0   1   1 | 0  1  1 1
-------------------------------------+----+------------+-------------------------+-------------------------------------+-----------------------------------------+------------------------------+----------
... xo. ox. ... oo.3ox. *e3xo.&#zx & ♦ 16 |  8  24  48 |  0  16   0  48   96   0 |   4   0  12   48   32  24    0    0 |  0  0   6  16   0   4   0    0   0    0 | 48   *  *  *   *   *   *   * | 1  0  1 0
... xo. ... oo.3oo.3ox.    ...&#x  & ♦  6 |  1   6   8 |  0   4   0   4   12   0 |   1   0   0    6    8   0    0    0 |  0  0   0   4   2   0   0    0   0    0 |  * 192  *  *   *   *   *   * | 1  0  1 0
... ... ... oo.3oo.3ox. *e3xo.&#x  & ♦ 16 |  0  48  32 |  0  64   0   0   96   0 |  32   0   0    0   64  24    0    0 |  2  0   0   0  16   8   0    0   0    0 |  *   * 24  *   *   *   *   * | 1  0  0 1
xxo xox oxx ... ... ...    ...&#x    ♦ 12 | 12   0  24 |  3   0  12  24    0   8 |   0  12   6    0    0   0   12    0 |  0  3   0   0   0   0   6    0   0    0 |  *   *  * 96   *   *   *   * | 0  2  0 0
xxo xox ... oox ... oxo    ...&#x  & ♦ 12 |  8   4  32 |  1   0   8  24   24  16 |   0   4   4   12    0   4   16   16 |  0  0   1   0   0   0   4    8   0    4 |  *   *  *  * 288   *   *   * | 0  1  1 0	prism A-(BC)
xxo ... ... oox3ooo ...    ...&#x  & ♦  7 |  2   3  14 |  0   1   1   6   12   6 |   0   0   0    6    4   0    3    6 |  0  0   0   2   0   0   0    3   2    0 |  *   *  *  *   * 384   *   * | 0  0  2 0
... ... ... oox3ooo3oxo    ...&#x  & ♦  9 |  0  12  20 |  0   8   0   0   36  12 |   2   0   0    0   16   6    0   24 |  0  0   0   0   2   1   0    0   8    6 |  *   *  *  *   *   * 192   * | 0  0  1 1
... ... ... oox ... oxo    xoo&#x    ♦  6 |  0   3  12 |  0   0   0   0   12   8 |   0   0   0    0    0   3    0   12 |  0  0   0   0   0   0   0    0   0    6 |  *   *  *  *   *   *   * 192 | 0  1  0 1
-------------------------------------+----+------------+-------------------------+-------------------------------------+-----------------------------------------+------------------------------+----------
... xo. ox. oo.3oo.3ox. *e3xo.&#zx & ♦ 32 | 16  96 128 |  0 128   0 128  384   0 |  64   0  32  192  256  96    0    0 |  4  0  24 128  64  32   0    0   0    0 |  8  32  4  0   0   0   0   0 | 6  *  * *
xxo xox oxx oox ... oxo    xoo&#zx   ♦ 24 | 24  12  96 |  6   0  48  96   96  64 |   0  48  24   48    0  24   96   96 |  0 12   6   0   0   0  48   48   0   48 |  0   0  0  8  12   0   0   8 | * 24  * *
xxo xox ... oox3ooo3oxo    ...&#x  & ♦ 20 | 12  24  80 |  1  16  16  64  144  48 |   4   8  12   72   64  24   48   96 |  0  0   6  32   8   4  12   48  32   24 |  1   4  0  0   6  16   4   0 | *  * 48 *
... ... ... oox3ooo3oxo *e3xoo&#zx   ♦ 24 |  0  72  96 |  0  96   0   0  288  96 |  48   0   0    0  192  72    0  288 |  3  0   0   0  48  24   0    0  96  144 |  0   0  3  0   0   0  24  24 | *  *  * 8

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