Acronym pabacca pin
Name partially bicontracted celliprismated penteract
Circumradius ...
Lace city
in approx. ASCII-art
       o3o4x  x3o4x  o3o4x               -- pacsid pith
                                 
                                 
                                 
o3o4x         u3o4x         o3o4x        -- pacsid pith variant
                                 
                                 
                                 
x3o4x  u3o4x  x3x4x  u3o4x  x3o4x        -- pacprit
                                 
                                 
                                 
o3o4x         u3o4x         o3o4x        -- pacsid pith variant
                                 
                                 
                                 
       o3o4x  x3o4x  o3o4x               -- pacsid pith
Coordinates
  • (sqrt(2), sqrt(2)/2; 1/2, 1/2, 1/2)                         & all permutations within all first 2 coords, all changes of sign
  • (sqrt(2), 0; 1/2, 1/2, (1+sqrt(2))/2)                     & all permutations within each coord subset, all changes of sign
  • (1/sqrt(2), 0; 1/2, 1/2, (1+2 sqrt(2))/2)               & all permutations within each coord subset, all changes of sign
  • (0, 0; 1/2, (1+sqrt(2))/2, (1+2 sqrt(2))/2)           & all permutations within all but first 2 coords, all changes of sign
Confer
uniform relative:
tot   cappin  
general polytopal classes:
partial Stott expansions  

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


Incidence matrix according to Dynkin symbol

qooo4xuxo oxux3ooox4xxxx&#zxt

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

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