Acronym pacca pin
Name partially contracted 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
                                 
                                 
                                 
                                 
                                 
x3o4x  u3o4x  x3x4x  u3o4x  x3o4x        -- pacprit
                                 
                                 
                                 
o3o4x         u3o4x         o3o4x        -- pacsid pith variant
                                 
                                 
                                 
       o3o4x  x3o4x  o3o4x               -- pacsid pith

  |      |      |      |      +-- x3o3o4x (sidpith)
  |      |      |      +--------- u3o3o4x (sidpith variant)
  |      |      +---------------- x3x3o4x (prit)
  |      +----------------------- u3o3o4x (sidpith variant)
  +------------------------------ x3o3o4x (sidpith)
Coordinates
  • (sqrt(2); 1/2, 1/2, 1/2, (1+sqrt(2))/2)                     & all permutations within all but first coord, all changes of sign
  • (1/sqrt(2); 1/2, 1/2, 1/2, (1+2 sqrt(2))/2)               & all permutations within all but first coord, all changes of sign
  • (0; 1/2, 1/2, (1+sqrt(2))/2, (1+2 sqrt(2))/2)           & all permutations within all but first coord, all changes of sign
Confer
uniform relative:
tot   cappin   prittip  
general polytopal classes:
partial Stott expansions  

This CRF polyteron can be obtained from cappin by partial Stott contraction only within an axial direction. In fact it happens to be just its removal of the medial segment prittip.


Incidence matrix according to Dynkin symbol

Qqo xux3oox3ooo4xxx&#zxt

o.. o..3o..3o..4o..     | 128   *   * |   3   3   4   1   1  0   0   0 |   3   6  3   3   3  0   0   0  0  0  0  0  0 |  1  3  3  1   3   6  3  0   0   0  0  0  0  0 | 1  1  3  3  1 0
.o. .o.3.o.3.o.4.o.     |   * 128   * |   0   0   1   3   3  0   0   0 |   0   0  0   3   3  3   3   6  0  0  0  0  0 |  0  0  0  0   3   6  3  1   1   3  3  0  0  0 | 0  1  3  3  1 1
..o ..o3..o3..o4..o     |   *   * 192 |   0   0   0   0   2  1   2   2 |   0   0  0   2   0  0   6   4  2  2  1  2  1 |  0  0  0  0   4   4  0  0   2   4  2  1  2  1 | 0  2  4  2  0 1
------------------------+-------------+--------------------------------+----------------------------------------------+-----------------------------------------------+----------------
... x.. ... ... ...     |   2   0   0 | 192   *   *   *   *  *   *   * |   2   2  0   1   0  0   0   0  0  0  0  0  0 |  1  2  1  0   2   2  0  0   0   0  0  0  0  0 | 1  1  2  1  0 0
... ... ... ... x..     |   2   0   0 |   * 192   *   *   *  *   *   * |   0   2  2   0   1  0   0   0  0  0  0  0  0 |  0  1  2  1   0   2  2  0   0   0  0  0  0  0 | 1  0  1  2  1 0
oo. oo.3oo.3oo.4oo.&#x  |   1   1   0 |   *   * 128   *   *  *   *   * |   0   0  0   3   3  0   0   0  0  0  0  0  0 |  0  0  0  0   3   6  3  0   0   0  0  0  0  0 | 0  1  3  3  1 0
... ... ... ... .x.     |   0   2   0 |   *   *   * 192   *  *   *   * |   0   0  0   0   1  2   0   2  0  0  0  0  0 |  0  0  0  0   0   2  2  1   0   1  2  0  0  0 | 0  0  1  2  1 1
.oo .oo3.oo3.oo4.oo&#x  |   0   1   1 |   *   *   *   * 384  *   *   * |   0   0  0   1   0  0   2   2  0  0  0  0  0 |  0  0  0  0   2   2  0  0   1   2  1  0  0  0 | 0  1  2  1  0 1
... ..x ... ... ...     |   0   0   2 |   *   *   *   *   * 96   *   * |   0   0  0   2   0  0   0   0  2  2  0  0  0 |  0  0  0  0   4   4  0  0   0   0  0  1  2  1 | 0  2  4  2  0 0
... ... ..x ... ...     |   0   0   2 |   *   *   *   *   *  * 192   * |   0   0  0   0   0  0   2   0  1  0  1  1  0 |  0  0  0  0   2   0  0  0   2   2  0  1  1  0 | 0  2  2  0  0 1
... ... ... ... ..x     |   0   0   2 |   *   *   *   *   *  *   * 192 |   0   0  0   0   0  0   0   2  0  1  0  1  1 |  0  0  0  0   0   2  0  0   0   2  2  0  1  1 | 0  0  2  2  0 1
------------------------+-------------+--------------------------------+----------------------------------------------+-----------------------------------------------+----------------
... x..3o.. ... ...     |   3   0   0 |   3   0   0   0   0  0   0   0 | 128   *  *   *   *  *   *   *  *  *  *  *  * |  1  1  0  0   1   0  0  0   0   0  0  0  0  0 | 1  1  1  0  0 0
... x.. ... ... x..     |   4   0   0 |   2   2   0   0   0  0   0   0 |   * 192  *   *   *  *   *   *  *  *  *  *  * |  0  1  1  0   0   1  0  0   0   0  0  0  0  0 | 1  0  1  1  0 0
... ... ... o..4x..     |   4   0   0 |   0   4   0   0   0  0   0   0 |   *   * 96   *   *  *   *   *  *  *  *  *  * |  0  0  1  1   0   0  1  0   0   0  0  0  0  0 | 1  0  0  1  1 0
... xux ... ... ...&#xt |   2   2   2 |   1   0   2   0   2  1   0   0 |   *   *  * 192   *  *   *   *  *  *  *  *  * |  0  0  0  0   2   2  0  0   0   0  0  0  0  0 | 0  1  2  1  0 0
... ... ... ... xx.&#x  |   2   2   0 |   0   1   2   1   0  0   0   0 |   *   *  *   * 192  *   *   *  *  *  *  *  * |  0  0  0  0   0   2  2  0   0   0  0  0  0  0 | 0  0  1  2  1 0
... ... ... .o.4.x.     |   0   4   0 |   0   0   0   4   0  0   0   0 |   *   *  *   *   * 96   *   *  *  *  *  *  * |  0  0  0  0   0   0  1  1   0   0  1  0  0  0 | 0  0  0  1  1 1
... ... .ox ... ...&#x  |   0   1   3 |   0   0   0   0   2  0   1   0 |   *   *  *   *   *  * 384   *  *  *  *  *  * |  0  0  0  0   1   0  0  0   1   1  0  0  0  0 | 0  1  1  0  0 1
... ... ... ... .xx&#x  |   0   2   2 |   0   0   0   1   2  0   0   1 |   *   *  *   *   *  *   * 384  *  *  *  *  * |  0  0  0  0   0   1  0  0   0   1  1  0  0  0 | 0  0  1  1  0 1
... ..x3..x ... ...     |   0   0   6 |   0   0   0   0   0  3   3   0 |   *   *  *   *   *  *   *   * 64  *  *  *  * |  0  0  0  0   2   0  0  0   0   0  0  1  1  0 | 0  2  2  0  0 0
... ..x ... ... ..x     |   0   0   4 |   0   0   0   0   0  2   0   2 |   *   *  *   *   *  *   *   *  * 96  *  *  * |  0  0  0  0   0   2  0  0   0   0  0  0  1  1 | 0  0  2  2  0 0
... ... ..x3..o ...     |   0   0   3 |   0   0   0   0   0  0   3   0 |   *   *  *   *   *  *   *   *  *  * 64  *  * |  0  0  0  0   0   0  0  0   2   0  0  1  0  0 | 0  2  0  0  0 1
... ... ..x ... ..x     |   0   0   4 |   0   0   0   0   0  0   2   2 |   *   *  *   *   *  *   *   *  *  *  * 96  * |  0  0  0  0   0   0  0  0   0   2  0  0  1  0 | 0  0  2  0  0 1
... ... ... ..o4..x     |   0   0   4 |   0   0   0   0   0  0   0   4 |   *   *  *   *   *  *   *   *  *  *  *  * 48 |  0  0  0  0   0   0  0  0   0   0  2  0  0  1 | 0  0  0  2  0 1
------------------------+-------------+--------------------------------+----------------------------------------------+-----------------------------------------------+----------------
... x..3o..3o.. ...        4   0   0 |   6   0   0   0   0  0   0   0 |   4   0  0   0   0  0   0   0  0  0  0  0  0 | 32  *  *  *   *   *  *  *   *   *  *  *  *  * | 1  1  0  0  0 0
... x..3o.. ... x..        6   0   0 |   6   3   0   0   0  0   0   0 |   2   3  0   0   0  0   0   0  0  0  0  0  0 |  * 64  *  *   *   *  *  *   *   *  *  *  *  * | 1  0  1  0  0 0
... x.. ... o..4x..        8   0   0 |   4   8   0   0   0  0   0   0 |   0   4  2   0   0  0   0   0  0  0  0  0  0 |  *  * 48  *   *   *  *  *   *   *  *  *  *  * | 1  0  0  1  0 0
... ... o..3o..4x..        8   0   0 |   0  12   0   0   0  0   0   0 |   0   0  6   0   0  0   0   0  0  0  0  0  0 |  *  *  * 16   *   *  *  *   *   *  *  *  *  * | 1  0  0  0  1 0
... xux3oox ... ...&#xt    3   3   6 |   3   0   3   0   6  3   3   0 |   1   0  0   3   0  0   3   0  1  0  0  0  0 |  *  *  *  * 128   *  *  *   *   *  *  *  *  * | 0  1  1  0  0 0
... xux ... ... xxx&#xt    4   4   4 |   2   2   4   2   4  2   0   2 |   0   1  0   2   2  0   0   2  0  1  0  0  0 |  *  *  *  *   * 192  *  *   *   *  *  *  *  * | 0  0  1  1  0 0
... ... ... oo.4xx.&#x     4   4   0 |   0   4   4   4   0  0   0   0 |   0   0  1   0   4  1   0   0  0  0  0  0  0 |  *  *  *  *   *   * 96  *   *   *  *  *  *  * | 0  0  0  1  1 0
... ... .o.3.o.4.x.        0   8   0 |   0   0   0  12   0  0   0   0 |   0   0  0   0   0  6   0   0  0  0  0  0  0 |  *  *  *  *   *   *  * 16   *   *  *  *  *  * | 0  0  0  0  1 1
... ... .ox3.oo ...&#x     0   1   3 |   0   0   0   0   3  0   3   0 |   0   0  0   0   0  0   3   0  0  0  1  0  0 |  *  *  *  *   *   *  *  * 128   *  *  *  *  * | 0  1  0  0  0 1
... ... .ox ... .xx&#x     0   2   4 |   0   0   0   1   4  0   2   2 |   0   0  0   0   0  0   2   2  0  0  0  1  0 |  *  *  *  *   *   *  *  *   * 192  *  *  *  * | 0  0  1  0  0 1
... ... ... .oo4.xx&#x     0   4   4 |   0   0   0   4   4  0   0   4 |   0   0  0   0   0  1   0   4  0  0  0  0  1 |  *  *  *  *   *   *  *  *   *   * 96  *  *  * | 0  0  0  1  0 1
... ..x3..x3..o ...        0   0  12 |   0   0   0   0   0  6  12   0 |   0   0  0   0   0  0   0   0  4  0  4  0  0 |  *  *  *  *   *   *  *  *   *   *  * 16  *  * | 0  2  0  0  0 0
... ..x3..x ... ..x        0   0  12 |   0   0   0   0   0  6   6   6 |   0   0  0   0   0  0   0   0  2  3  0  3  0 |  *  *  *  *   *   *  *  *   *   *  *  * 32  * | 0  0  2  0  0 0
... ..x ... ..o4..x        0   0   8 |   0   0   0   0   0  4   0   8 |   0   0  0   0   0  0   0   0  0  4  0  0  2 |  *  *  *  *   *   *  *  *   *   *  *  *  * 24 | 0  0  0  2  0 0
------------------------+-------------+--------------------------------+----------------------------------------------+-----------------------------------------------+----------------
... x..3o..3o..4x..       64   0   0 |  96  96   0   0   0  0   0   0 |  64  96 48   0   0  0   0   0  0  0  0  0  0 | 16 32 24  8   0   0  0  0   0   0  0  0  0  0 | 2  *  *  *  * *
... xux3oox3ooo ...&#xt    4   4  12 |   6   0   4   0  12  6  12   0 |   4   0  0   6   0  0  12   0  4  0  4  0  0 |  1  0  0  0   4   0  0  0   4   0  0  1  0  0 | * 32  *  *  * *
... xux3oox ... xxx&#xt    6   6  12 |   6   3   6   3  12  6   6   6 |   2   3  0   6   3  0   6   6  2  3  0  3  0 |  0  1  0  0   2   3  0  0   0   3  0  0  1  0 | *  * 64  *  * *
... xux ... ooo4xxx&#xt    8   8   8 |   4   8   8   8   8  4   0   8 |   0   4  2   4   8  2   0   8  0  4  0  0  2 |  0  0  1  0   0   4  2  0   0   0  2  0  0  1 | *  *  * 48  * *
... ... oo.3oo.4xx.&#x     8   8   0 |   0  12   8  12   0  0   0   0 |   0   0  6   0  12  6   0   0  0  0  0  0  0 |  0  0  0  1   0   0  6  1   0   0  0  0  0  0 | *  *  *  * 16 *
.qo ... .ox3.oo4.xx&#zx    0  16  24 |   0   0   0  24  48  0  24  24 |   0   0  0   0   0 12  48  48  0  0  8 12  6 |  0  0  0  0   0   0  0  2  16  24 12  0  0  0 | *  *  *  *  * 8

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