Acronym sadlaq
Name hepteract-diminished pentacontihexapentacosiheptacontihexaexon
Circumradius 1
Lace hyper city
in approx. ASCII-art 
         
  O   E  
         
  E   O  
         

    N    
         
N   T   N
         
    N    

         
  O   E  
         
  E   O  
         

i.e. ihdlaq with a central tes

where:
N = o3o3o *b3x (= x3o3o4o, hex)
E = x3o3o *b3o (gyro hex)
O = o3o3x *b3o (alt. gyro hex)
T = qo3oo3oq *b3oo&#x (= o3o3o4x, tes)
Coordinates
    • (sqrt(2); 1, 1; 1, 1; 1, 1)/sqrt(8)       & both signs in first and all even changes of sign in all other coords
      (2 × 32 = 64 vertices: top and bottom hax)
    • (0; 1, 0; 1, 0; 0, 0)/sqrt(2)               & all permutations within each block and of all but first blocks, all changes of sign
      (3 × 4 × 4 = 48 vertices: equatorial xedrag)
    • (1, 1, 1, 1, 0, 0, 0)/2       & all sign changes
    • (1, 1, 0, 0, 1, 1, 0)/2       & all sign changes
    • (1, 0, 1, 0, 1, 0, 1)/2       & all sign changes
    • (1, 0, 0, 1, 0, 1, 1)/2       & all sign changes
    • (0, 0, 1, 1, 1, 1, 0)/2       & all sign changes
    • (0, 1, 0, 1, 1, 0, 1)/2       & all sign changes
    • (0, 1, 1, 0, 0, 1, 1)/2       & all sign changes
Face vector 112, 1568, 6720, 11200, 7924, 2184, 198
Confer
uniform relative:
laq  
related scaliform:
ihdlaq  
general polytopal classes:
scaliform  
External
links 		polytopewiki

This polyexon is obtained by diminishing laq at the 14 vertices of a vertex inscribed q-zee or equivalently by the 14 facets of a (unit) hept.


Incidence matrix according to Dynkin symbol

xxxxooo xxoooxx xoxoxox xooxxxo oxxoxxo oxoxxox ooxxoxx&#zx → heights = 0
(tegum sum of haxip (first 4 layers) and an equatorial xedrag (last 3 layers) — or equivalently:
 tegum sum of 7 interlocking (unit) tes)

o...... o...... o...... o...... o...... o...... o......      & | 112 |   4   24 |   72  12   96 |   48  192  32  128 |  120   80  120  6  48 |  24  48  54  24 |   8  4 12
---------------------------------------------------------------+-----+----------+---------------+--------------------+-----------------------+-----------------+----------
x...... ....... ....... ....... ....... ....... .......      & |   2 | 224    * ♦   12   0    0 |   12   24   0    0 |   24    8    0  3  12 |   6   0  12  12 |   0  3  6
oo..... oo..... oo..... oo..... oo..... oo..... oo.....&#x   & |   2 |   * 1344 |    4   1    8 |    4   12   4   16 |   16   12   20  1  10 |   4  10  14   8 |   2  2  6
---------------------------------------------------------------+-----+----------+---------------+--------------------+-----------------------+-----------------+----------
....... ....... xo..... ....... ....... ....... .......&#x   & |   3 |   1    2 | 2688   *    * |    2    4   0    0 |    6    2    0  1   4 |   2   0   5   6 |   0  2  4
ooo.... ooo.... ooo.... ooo.... ooo.... ooo.... ooo....&#x   & |   3 |   0    3 |    * 448    * ♦    0    0   0    8 |    0    4   12  0   0 |   0   8   6   0 |   2  0  4  type A
ooo.... ooo.... ooo.... ooo.... ooo.... ooo.... ooo....&#x   & |   3 |   0    3 |    *   * 3584 |    0    3   1    3 |    3    3    6  0   3 |   1   4   6   3 |   1  1  4  type B
---------------------------------------------------------------+-----+----------+---------------+--------------------+-----------------------+-----------------+----------
....... ....... xo..... ....... ox..... ....... .......&#x   & ♦   4 |   2    4 |    4   0    0 | 1344    *   *    * |    2    0    0  1   2 |   1   0   2   5 |   0  2  3
....... ....... ....... xoo.... ....... ....... .......&#x   & ♦   4 |   1    3 |    2   0    2 |    * 5376   *    * |    2    1    0  0   1 |   1   0   3   2 |   0  1  3
oooo... oooo... oooo... oooo... oooo... oooo... oooo...&#x   & ♦   4 |   0    6 |    0   0    4 |    *    * 896    * |    0    0    3  0   3 |   0   3   3   3 |   1  1  3  type A
oooo... oooo... oooo... oooo... oooo... oooo... oooo...&#x   & ♦   4 |   0    6 |    0   1    3 |    *    *   * 3584 |    0    1    3  0   0 |   0   3   3   0 |   1  0  3  type B
---------------------------------------------------------------+-----+----------+---------------+--------------------+-----------------------+-----------------+----------
....... ....... xo.o... ....... ox.o... ....... .......&#x   & ♦   5 |   2    8 |    6   0    4 |    1    4   0    0 | 2688    *    *  *   * |   1   0   1   1 |   0  1  2
....... ....... ....... xoo...o ....... ....... .......&#x   & ♦   5 |   1    9 |    3   1    6 |    0    3   0    2 |    * 1792    *  *   * |   0   0   3   0 |   0  0  3
ooooo.. ooooo.. ooooo.. ooooo.. ooooo.. ooooo.. ooooo..&#x   & ♦   5 |   0   10 |    0   2    8 |    0    0   1    4 |    *    * 2688  *   * |   0   2   1   0 |   1  0  2
....... ....... xo..... xo..... ox..... ox..... .......&#zx  & ♦   8 |   8   16 |   32   0    0 |   16    0   0    0 |    *    *    * 84   * |   0   0   0   4 |   0  2  2
....... ....... xoxo... ....... ....... oxox... .......&#xr  & ♦   8 |   4   20 |   16   0   16 |    4    8   4    0 |    *    *    *  * 672 |   0   0   1   2 |   0  1  2
---------------------------------------------------------------+-----+----------+---------------+--------------------+-----------------------+-----------------+----------
....... ....... xo.o... ....... ox.o... ....... oo.x...&#x   & ♦   6 |   3   12 |   12   0    8 |    3   12   0    0 |    6    0    0  0   0 | 448   *   *   * |   0  1  1
oooooo. oooooo. oooooo. oooooo. oooooo. oooooo. oooooo.&#x   & ♦   6 |   0   15 |    0   4   16 |    0    0   3   12 |    0    0    6  0   0 |   * 896   *   * |   1  0  1
....... .......(xoxo)o. ....... .......(oxox)o. .......&#xrt & ♦   9 |   4   28 |   20   4   32 |    4   24   4   16 |    4    8    4  0   1 |   *   * 672   * |   0  0  2
....... ....... xoxo... xoox... oxxo... oxox... .......&#zxt & ♦  16 |  16   64 |   96   0   64 |   40   64  16    0 |   16    0    0  2   8 |   *   *   * 168 |   0  1  1  prism (AB)(CD)
---------------------------------------------------------------+-----+----------+---------------+--------------------+-----------------------+-----------------+----------
ooooooo ooooooo ooooooo ooooooo ooooooo ooooooo ooooooo&#x     ♦   7 |   0   21 |    0   7   28 |    0    0   7   28 |    0    0   21  0   0 |   0   7   0   0 | 128  *  *
....... xxoo... xoxo... xoox... oxxo... oxox... ooxx...&#zx  & ♦  32 |  48  192 |  384   0  256 |  192  384  64    0 |  192    0    0 12  48 |  32   0   0  12 |   * 14  *
....... ....... xoxo.ox xoox.xo oxxo.xo oxox.ox .......&#zxr & ♦  24 |  24  144 |  192  32  256 |   72  288  48  192 |   96   96   96  3  24 |   8  16  24   3 |   *  * 56  trigonism (AB)(CD)(FG)

© 2004-2024
top of page