Acronym pabextot
Name partially biexpanded truncated triacontaditeron
Circumradius ...
Lace city
in approx. ASCII-art 
       o3o4o  x3o4o      x3o4o  o3o4o       		-- ((wx ox3oo4oo))&#zx (pex hex)
                                            
                                            
                                            
o3o4o         u3o4o      u3o4o         o3o4o		-- ((Xx ou3oo4oo))&#zu (pex hex variant)
                                            
                                            
                                            
x3o4o  u3o4o  x3x4o      x3x4o  u3o4o  x3o4o		-- ((Xwx xux3oox4ooo))&#zxt (pex thex)
                                            
                                            
                                            
                                            
                                            
x3o4o  u3o4o  x3x4o      x3x4o  u3o4o  x3o4o		-- ((Xwx xux3oox4ooo))&#zxt (pex thex)
                                            
                                            
                                            
o3o4o         u3o4o      u3o4o         o3o4o		-- ((Xx ou3oo4oo))&#zu (pex hex variant)
                                            
                                            
                                            
       o3o4o  x3o4o      x3o4o  o3o4o       		-- ((wx ox3oo4oo))&#zx (pex hex)

where:
X = w+q = x+2q, u=2x
Coordinates
  • (0, 0, 0; (1+sqrt(2))/2, (1+2 sqrt(2))/2)         & all permutations within last 2 coords, all changes of sign
  • (1/sqrt(2), 0, 0; 1/2, (1+2 sqrt(2))/2)             & all permutations within each subset, all changes of sign
  • (sqrt(2), 0, 0; 1/2, (1+sqrt(2))/2)                   & all permutations within each subset, all changes of sign
  • (sqrt(2), 1/sqrt(2), 0; 1/2, 1/2)                       & all permutations within all but last coord, all changes of sign
Face vector 200, 700, 936, 516, 82
Confer
uniform relative:
tot   cappin  
general polytopal classes:
partial Stott expansions  

This CRF polyteron can be obtained from tot by partial Stott expansion only within 2 orthogonal axial directions.


Incidence matrix according to Dynkin symbol

((wxxx4xuxo oxux3ooox4oooo))&#zxt

  o...4o... o...3o...4o...        | 8  *  *  * | 1  6  0  0  0  0  0   0  0  0  0 |  6 12  0  0  0  0  0  0   0  0  0  0  0 | 12  8  0  0  0  0  0  0  0  0 | 1  8  0 0 0
  .o..4.o.. .o..3.o..4.o..        | * 48  *  * | 0  1  1  4  1  0  0   0  0  0  0 |  1  4  4  4  1  4  0  0   0  0  0  0  0 |  4  4  4  4  4  0  0  0  0  0 | 1  4  4 0 0
  ..o.4..o. ..o.3..o.4..o.        | *  * 48  * | 0  0  0  0  1  1  1   4  0  0  0 |  1  0  0  0  1  4  4  4   4  0  0  0  0 |  4  0  0  4  4  4  4  0  0  0 | 0  4  4 1 0
  ...o4...o ...o3...o4...o        | *  *  * 96 | 0  0  0  0  0  0  0   2  2  1  2 |  0  0  0  0  0  2  2  1   4  1  2  4  2 |  1  0  0  2  4  4  2  1  2  4 | 0  2  4 1 2
----------------------------------+------------+----------------------------------+-----------------------------------------+-------------------------------+------------
  .... x... .... .... ....        | 2  0  0  0 | 4  *  *  *  *  *  *   *  *  *  * ♦  6  0  0  0  0  0  0  0   0  0  0  0  0 | 12  0  0  0  0  0  0  0  0  0 | 0  8  0 0 0
  oo..4oo.. oo..3oo..4oo..  &#x   | 1  1  0  0 | * 48  *  *  *  *  *   *  *  *  * |  1  4  0  0  0  0  0  0   0  0  0  0  0 |  4  4  0  0  0  0  0  0  0  0 | 1  4  0 0 0
  .x.. .... .... .... ....        | 0  2  0  0 | *  * 24  *  *  *  *   *  *  *  * |  0  0  4  0  1  0  0  0   0  0  0  0  0 |  0  0  4  4  0  0  0  0  0  0 | 1  0  4 0 0
  .... .... .x.. .... ....        | 0  2  0  0 | *  *  * 96  *  *  *   *  *  *  * |  0  1  1  2  0  1  0  0   0  0  0  0  0 |  1  2  2  1  2  0  0  0  0  0 | 1  2  2 0 0
  .oo.4.oo. .oo.3.oo.4.oo.  &#x   | 0  1  1  0 | *  *  *  * 48  *  *   *  *  *  * |  1  0  0  0  1  4  0  0   0  0  0  0  0 |  4  0  0  4  4  0  0  0  0  0 | 0  4  4 0 0
  ..x. .... .... .... ....        | 0  0  2  0 | *  *  *  *  * 24  *   *  *  *  * |  0  0  0  0  1  0  4  0   0  0  0  0  0 |  0  0  0  4  0  4  0  0  0  0 | 0  0  4 1 0
  .... ..x. .... .... ....        | 0  0  2  0 | *  *  *  *  *  * 24   *  *  *  * |  1  0  0  0  0  0  0  4   0  0  0  0  0 |  4  0  0  0  0  0  4  0  0  0 | 0  4  0 1 0
  ..oo4..oo ..oo3..oo4..oo  &#x   | 0  0  1  1 | *  *  *  *  *  *  * 192  *  *  * |  0  0  0  0  0  1  1  1   2  0  0  0  0 |  1  0  0  1  2  2  2  0  0  0 | 0  2  2 1 0
  ...x .... .... .... ....        | 0  0  0  2 | *  *  *  *  *  *  *   * 96  *  * |  0  0  0  0  0  0  1  0   0  1  1  2  0 |  0  0  0  1  0  2  0  1  2  2 | 0  0  2 1 2
  .... .... ...x .... ....        | 0  0  0  2 | *  *  *  *  *  *  *   *  * 48  * |  0  0  0  0  0  2  0  0   0  0  2  0  2 |  1  0  0  2  4  0  0  1  0  4 | 0  2  4 0 2
  .... .... .... ...x ....        | 0  0  0  2 | *  *  *  *  *  *  *   *  *  * 96 |  0  0  0  0  0  0  0  0   2  0  0  2  1 |  0  0  0  0  2  2  1  0  1  2 | 0  1  2 1 1
----------------------------------+------------+----------------------------------+-----------------------------------------+-------------------------------+------------
  .... xux. .... .... ....  &#xt  | 2  2  2  0 | 1  2  0  0  2  0  1   0  0  0  0 | 24  *  *  *  *  *  *  *   *  *  *  *  * |  4  0  0  0  0  0  0  0  0  0 | 0  4  0 0 0
  .... .... ox.. .... ....  &#x   | 1  2  0  0 | 0  2  0  1  0  0  0   0  0  0  0 |  * 96  *  *  *  *  *  *   *  *  *  *  * |  1  2  0  0  0  0  0  0  0  0 | 1  2  0 0 0
  .x.. .... .x.. .... ....        | 0  4  0  0 | 0  0  2  2  0  0  0   0  0  0  0 |  *  * 48  *  *  *  *  *   *  *  *  *  * |  0  0  2  1  0  0  0  0  0  0 | 1  0  2 0 0
  .... .... .x..3.o.. ....        | 0  3  0  0 | 0  0  0  3  0  0  0   0  0  0  0 |  *  *  * 64  *  *  *  *   *  *  *  *  * |  0  1  1  0  1  0  0  0  0  0 | 1  1  1 0 0
  .xx. .... .... .... ....  &#x   | 0  2  2  0 | 0  0  1  0  2  1  0   0  0  0  0 |  *  *  *  * 24  *  *  *   *  *  *  *  * |  0  0  0  4  0  0  0  0  0  0 | 0  0  4 0 0
  .... .... .xux .... ....  &#xt  | 0  2  2  2 | 0  0  0  1  2  0  0   2  0  1  0 |  *  *  *  *  * 96  *  *   *  *  *  *  * |  1  0  0  1  2  0  0  0  0  0 | 0  2  2 0 0
  ..xx .... .... .... ....  &#x   | 0  0  2  2 | 0  0  0  0  0  1  0   2  1  0  0 |  *  *  *  *  *  * 96  *   *  *  *  *  * |  0  0  0  1  0  2  0  0  0  0 | 0  0  2 1 0
  .... ..xo .... .... ....  &#x   | 0  0  2  1 | 0  0  0  0  0  0  1   2  0  0  0 |  *  *  *  *  *  *  * 96   *  *  *  *  * |  1  0  0  0  0  0  2  0  0  0 | 0  2  0 1 0
  .... .... .... ..ox ....  &#x   | 0  0  1  2 | 0  0  0  0  0  0  0   2  0  0  1 |  *  *  *  *  *  *  *  * 192  *  *  *  * |  0  0  0  0  1  1  1  0  0  0 | 0  1  1 1 0
  ...x4...o .... .... ....        | 0  0  0  4 | 0  0  0  0  0  0  0   0  4  0  0 |  *  *  *  *  *  *  *  *   * 24  *  *  * |  0  0  0  0  0  0  0  1  2  0 | 0  0  0 1 2
  ...x .... ...x .... ....        | 0  0  0  4 | 0  0  0  0  0  0  0   0  2  2  0 |  *  *  *  *  *  *  *  *   *  * 48  *  * |  0  0  0  1  0  0  0  1  0  2 | 0  0  2 0 2
  ...x .... .... ...x ....        | 0  0  0  4 | 0  0  0  0  0  0  0   0  2  0  2 |  *  *  *  *  *  *  *  *   *  *  * 96  * |  0  0  0  0  0  1  0  0  1  1 | 0  0  1 1 1
  .... .... ...x3...x ....        | 0  0  0  6 | 0  0  0  0  0  0  0   0  0  3  3 |  *  *  *  *  *  *  *  *   *  *  *  * 32 |  0  0  0  0  2  0  0  0  0  2 | 0  1  2 0 1
----------------------------------+------------+----------------------------------+-----------------------------------------+-------------------------------+------------
  .... xuxo oxux .... ....  &#xt  ♦ 2  4  4  2 | 1  4  0  2  4  0  2   4  0  1  0 |  2  2  0  0  0  2  0  2   0  0  0  0  0 | 48  *  *  *  *  *  *  *  *  * | 0  2  0 0 0
  .... .... ox..3oo.. ....  &#x   ♦ 1  3  0  0 | 0  3  0  3  0  0  0   0  0  0  0 |  0  3  0  1  0  0  0  0   0  0  0  0  0 |  * 64  *  *  *  *  *  *  *  * | 1  1  0 0 0
  .x.. .... .x..3.o.. ....        ♦ 0  6  0  0 | 0  0  3  6  0  0  0   0  0  0  0 |  0  0  3  2  0  0  0  0   0  0  0  0  0 |  *  * 32  *  *  *  *  *  *  * | 1  0  1 0 0
  .xxx .... .xux .... ....  &#xt  ♦ 0  4  4  4 | 0  0  2  2  4  2  0   4  2  2  0 |  0  0  1  0  2  2  2  0   0  0  1  0  0 |  *  *  * 48  *  *  *  *  *  * | 0  0  2 0 0
  .... .... .xux3.oox ....  &#xt  ♦ 0  3  3  6 | 0  0  0  3  3  0  0   6  0  3  3 |  0  0  0  1  0  3  0  0   3  0  0  0  1 |  *  *  *  * 64  *  *  *  *  * | 0  1  1 0 0
  ..xx .... .... ..ox ....  &#x   ♦ 0  0  2  4 | 0  0  0  0  0  1  0   4  2  0  2 |  0  0  0  0  0  0  2  0   2  0  0  1  0 |  *  *  *  *  * 96  *  *  *  * | 0  0  1 1 0
  .... ..xo .... ..ox ....  &#x   ♦ 0  0  2  2 | 0  0  0  0  0  0  1   4  0  0  1 |  0  0  0  0  0  0  0  2   2  0  0  0  0 |  *  *  *  *  *  * 96  *  *  * | 0  1  0 1 0
  ...x4...o ...x .... ....        ♦ 0  0  0  8 | 0  0  0  0  0  0  0   0  8  4  0 |  0  0  0  0  0  0  0  0   0  2  4  0  0 |  *  *  *  *  *  *  * 12  *  * | 0  0  0 0 2
  ...x4...o .... ...x ....        ♦ 0  0  0  8 | 0  0  0  0  0  0  0   0  8  0  4 |  0  0  0  0  0  0  0  0   0  2  0  4  0 |  *  *  *  *  *  *  *  * 24  * | 0  0  0 1 1
  ...x .... ...x3...x ....        ♦ 0  0  0 12 | 0  0  0  0  0  0  0   0  6  6  6 |  0  0  0  0  0  0  0  0   0  0  3  3  2 |  *  *  *  *  *  *  *  *  * 32 | 0  0  1 0 1
----------------------------------+------------+----------------------------------+-----------------------------------------+-------------------------------+------------
((wx.. .... ox..3oo..4oo..))&#zx  ♦ 2 12  0  0 | 0 12  6 24  0  0  0   0  0  0  0 |  0 24 12 16  0  0  0  0   0  0  0  0  0 |  0 16  8  0  0  0  0  0  0  0 | 4  *  * * *
  .... xuxo oxux3ooox ....  &#xt  ♦ 2  6  6  6 | 1  6  0  6  6  0  3  12  0  3  3 |  3  6  0  2  0  6  0  6   6  0  0  0  1 |  3  2  0  0  2  0  3  0  0  0 | * 32  * * *
  .xxx .... .xux3.oox ....  &#xt  ♦ 0  6  6 12 | 0  0  3  6  6  3  0  12  6  6  6 |  0  0  3  2  3  6  6  0   6  0  3  3  2 |  0  0  1  3  2  3  0  0  0  1 | *  * 32 * *
((..xx4..xo .... ..ox4..oo))&#zx  ♦ 0  0  8 16 | 0  0  0  0  0  4  4  32 16  0 16 |  0  0  0  0  0  0 16 16  32  4  0 16  0 |  0  0  0  0  0 16 16  0  4  0 | *  *  * 6 *
  ...x4...o ...x3...x ....        ♦ 0  0  0 24 | 0  0  0  0  0  0  0   0 24 12 12 |  0  0  0  0  0  0  0  0   0  6 12 12  4 |  0  0  0  0  0  0  0  3  3  4 | *  *  * * 8

© 2004-2026
top of page