Acronym snan
Name snub penteract,
alternation of great cellated penteractitriacontiditeron
Circumradius ...
Confer
general polytopal classes:
isogonal  
External
links
polytopewiki

This isogonal polyteron is obtained by hemiation of gacnet. But because of lower degree of freedom the resulting edge sizes cannot be made all alike.


Incidence matrix according to Dynkin symbol

s3s3s3s4s

demi( . . . . . ) | 1920 |   1   1   1   1   1   1    2    2    2    2 |   1   1   1   1    3    3    3    3    3    3    3    3    3    3 |   1   1   1   1   1   1   1   1   1  1    4    4    4    4    4 |  1  1  1  1  1    5
------------------+------+---------------------------------------------+-------------------------------------------------------------------+-----------------------------------------------------------------+--------------------
      s 2 s . .   |    2 | 960   *   *   *   *   *    *    *    *    * |   0   0   0   0    2    0    0    2    2    0    0    0    0    0 |   1   0   0   1   1   0   0   0   0  0    2    2    0    2    0 |  1  1  0  1  0    1  q
      s 2 . s .   |    2 |   * 960   *   *   *   *    *    *    *    * |   0   0   0   0    0    2    0    2    0    2    0    0    0    0 |   0   1   0   1   0   1   0   0   0  0    2    0    2    2    0 |  1  0  1  1  0    1  q
      s . 2 . s   |    2 |   *   * 960   *   *   *    *    *    *    * |   0   0   0   0    0    0    2    0    2    2    0    0    0    0 |   0   0   1   0   1   1   0   0   0  0    0    2    2    2    0 |  0  1  1  1  0    1  q
      . s 2 s .   |    2 |   *   *   * 960   *   *    *    *    *    * |   0   0   0   0    0    2    0    0    0    0    2    0    2    0 |   0   1   0   0   0   0   1   0   1  0    2    0    2    0    2 |  1  0  1  0  1    1  q
      . s 2 . s   |    2 |   *   *   *   * 960   *    *    *    *    * |   0   0   0   0    0    0    2    0    0    0    0    2    2    0 |   0   0   1   0   0   0   0   1   1  0    0    2    2    0    2 |  0  1  1  0  1    1  q
      . . s 2 s   |    2 |   *   *   *   *   * 960    *    *    *    * |   0   0   0   0    0    0    0    0    2    0    0    2    0    2 |   0   0   0   0   1   0   0   1   0  1    0    2    0    2    2 |  0  1  0  1  1    1  q
sefa( s3s . . . ) |    2 |   *   *   *   *   *   * 1920    *    *    * |   1   0   0   0    1    1    1    0    0    0    0    0    0    0 |   1   1   1   0   0   0   0   0   0  0    1    1    1    0    0 |  1  1  1  0  0    1  h
sefa( . s3s . . ) |    2 |   *   *   *   *   *   *    * 1920    *    * |   0   1   0   0    1    0    0    0    0    0    1    1    0    0 |   1   0   0   0   0   0   1   1   0  0    1    1    0    0    1 |  1  1  0  0  1    1  h
sefa( . . s3s . ) |    2 |   *   *   *   *   *   *    *    * 1920    * |   0   0   1   0    0    0    0    1    0    0    1    0    0    1 |   0   0   0   1   0   0   1   0   0  1    1    0    0    1    1 |  1  0  0  1  1    1  h
sefa( . . . s4s ) |    2 |   *   *   *   *   *   *    *    *    * 1920 |   0   0   0   1    0    0    0    0    0    1    0    0    1    1 |   0   0   0   0   0   1   0   0   1  1    0    0    1    1    1 |  0  0  1  1  1    1  k
------------------+------+---------------------------------------------+-------------------------------------------------------------------+-----------------------------------------------------------------+--------------------
      s3s . . .   |    3 |   0   0   0   0   0   0    3    0    0    0 | 640   *   *   *    *    *    *    *    *    *    *    *    *    * |   1   1   1   0   0   0   0   0   0  0    0    0    0    0    0 |  1  1  1  0  0    0  h3o
      . s3s . .   |    3 |   0   0   0   0   0   0    0    3    0    0 |   * 640   *   *    *    *    *    *    *    *    *    *    *    * |   1   0   0   0   0   0   1   1   0  0    0    0    0    0    0 |  1  1  0  0  1    0  h3o
      . . s3s .   |    3 |   0   0   0   0   0   0    0    0    3    0 |   *   * 640   *    *    *    *    *    *    *    *    *    *    * |   0   0   0   1   0   0   1   0   0  1    0    0    0    0    0 |  1  0  0  1  1    0  h3o
      . . . s4s   |    4 |   0   0   0   0   0   0    0    0    0    4 |   *   *   * 480    *    *    *    *    *    *    *    *    *    * |   0   0   0   0   0   1   0   0   1  1    0    0    0    0    0 |  0  0  1  1  1    0  k4o
sefa( s3s3s . . ) |    3 |   1   0   0   0   0   0    1    1    0    0 |   *   *   *   * 1920    *    *    *    *    *    *    *    *    * |   1   0   0   0   0   0   0   0   0  0    1    1    0    0    0 |  1  1  0  0  0    1  oq&#h
sefa( s3s 2 s . ) |    3 |   0   1   0   1   0   0    1    0    0    0 |   *   *   *   *    * 1920    *    *    *    *    *    *    *    * |   0   1   0   0   0   0   0   0   0  0    1    0    1    0    0 |  1  0  1  0  0    1  oh&#q
sefa( s3s 2 . s ) |    3 |   0   0   1   0   1   0    1    0    0    0 |   *   *   *   *    *    * 1920    *    *    *    *    *    *    * |   0   0   1   0   0   0   0   0   0  0    0    1    1    0    0 |  0  1  1  0  0    1  oh&#q
sefa( s 2 s3s . ) |    3 |   1   1   0   0   0   0    0    0    1    0 |   *   *   *   *    *    *    * 1920    *    *    *    *    *    * |   0   0   0   1   0   0   0   0   0  0    1    0    0    1    0 |  1  0  0  1  0    1  oh&#q
sefa( s 2 s 2 s ) |    3 |   1   0   1   0   0   1    0    0    0    0 |   *   *   *   *    *    *    *    * 1920    *    *    *    *    * |   0   0   0   0   1   0   0   0   0  0    0    1    0    1    0 |  0  1  0  1  0    1  q3o
sefa( s 2 . s4s ) |    3 |   0   1   1   0   0   0    0    0    0    1 |   *   *   *   *    *    *    *    *    * 1920    *    *    *    * |   0   0   0   0   0   1   0   0   0  0    0    0    1    1    0 |  0  0  1  1  0    1  ok&#q
sefa( . s3s3s . ) |    3 |   0   0   0   1   0   0    0    1    1    0 |   *   *   *   *    *    *    *    *    *    * 1920    *    *    * |   0   0   0   0   0   0   1   0   0  0    1    0    0    0    1 |  1  0  0  0  1    1  oq&#h
sefa( . s3s 2 s ) |    3 |   0   0   0   0   1   1    0    1    0    0 |   *   *   *   *    *    *    *    *    *    *    * 1920    *    * |   0   0   0   0   0   0   0   1   0  0    0    1    0    0    1 |  0  1  0  0  1    1  oh&#q
sefa( . s 2 s4s ) |    3 |   0   0   0   1   1   0    0    0    0    1 |   *   *   *   *    *    *    *    *    *    *    *    * 1920    * |   0   0   0   0   0   0   0   0   1  0    0    0    1    0    1 |  0  0  1  0  1    1  ok&#q
sefa( . . s3s4s ) |    3 |   0   0   0   0   0   1    0    0    1    1 |   *   *   *   *    *    *    *    *    *    *    *    *    * 1920 |   0   0   0   0   0   0   0   0   0  1    0    0    0    1    1 |  0  0  0  1  1    1  (qhk)
------------------+------+---------------------------------------------+-------------------------------------------------------------------+-----------------------------------------------------------------+--------------------
      s3s3s . .   |   12 |   6   0   0   0   0   0   12   12    0    0 |   4   4   0   0   12    0    0    0    0    0    0    0    0    0 | 160   *   *   *   *   *   *   *   *  *    *    *    *    *    * |  1  1  0  0  0    0  pyritohedral ike variant
      s3s 2 s .   |    6 |   0   3   0   3   0   0    6    0    0    0 |   2   0   0   0    0    6    0    0    0    0    0    0    0    0 |   * 320   *   *   *   *   *   *   *  *    *    *    *    *    * |  1  0  1  0  0    0  triangular antiprism
      s3s 2 . s   |    6 |   0   0   3   0   3   0    6    0    0    0 |   2   0   0   0    0    0    6    0    0    0    0    0    0    0 |   *   * 320   *   *   *   *   *   *  *    *    *    *    *    * |  0  1  1  0  0    0  triangular antiprism
      s 2 s3s .   |    6 |   3   3   0   0   0   0    0    0    6    0 |   0   0   2   0    0    0    0    6    0    0    0    0    0    0 |   *   *   * 320   *   *   *   *   *  *    *    *    *    *    * |  1  0  0  1  0    0  triangular antiprism
      s 2 s 2 s   |    4 |   2   0   2   0   0   2    0    0    0    0 |   0   0   0   0    0    0    0    0    4    0    0    0    0    0 |   *   *   *   * 480   *   *   *   *  *    *    *    *    *    * |  0  1  0  1  0    0  q-tetrahedron
      s 2 . s4s   |    8 |   0   4   4   0   0   0    0    0    0    8 |   0   0   0   2    0    0    0    0    0    8    0    0    0    0 |   *   *   *   *   * 240   *   *   *  *    *    *    *    *    * |  0  0  1  1  0    0  shallow square antiprism
      . s3s3s .   |   12 |   0   0   0   6   0   0    0   12   12    0 |   0   4   4   0    0    0    0    0    0    0   12    0    0    0 |   *   *   *   *   *   * 160   *   *  *    *    *    *    *    * |  1  0  0  0  1    0  pyritohedral ike variant
      . s3s 2 s   |    6 |   0   0   0   0   3   3    0    6    0    0 |   0   2   0   0    0    0    0    0    0    0    0    6    0    0 |   *   *   *   *   *   *   * 320   *  *    *    *    *    *    * |  0  1  0  0  1    0  triangular antiprism
      . s 2 s4s   |    8 |   0   0   0   4   4   0    0    0    0    8 |   0   0   0   2    0    0    0    0    0    0    0    0    8    0 |   *   *   *   *   *   *   *   * 240  *    *    *    *    *    * |  0  0  1  0  1    0  shallow square antiprism
      . . s3s4s   |   24 |   0   0   0   0   0  12    0    0   24   24 |   0   0   8   6    0    0    0    0    0    0    0    0    0   24 |   *   *   *   *   *   *   *   *   * 80    *    *    *    *    * |  0  0  0  1  1    0  snub cube
sefa( s3s3s3s . ) |    4 |   1   1   0   1   0   0    1    1    1    0 |   0   0   0   0    1    1    0    1    0    0    1    0    0    0 |   *   *   *   *   *   *   *   *   *  * 1920    *    *    *    * |  1  0  0  0  0    1
sefa( s3s3s 2 s ) |    4 |   1   0   1   0   1   1    1    1    0    0 |   0   0   0   0    1    0    1    0    1    0    0    1    0    0 |   *   *   *   *   *   *   *   *   *  *    * 1920    *    *    * |  0  1  0  0  0    1
sefa( s3s 2 s4s ) |    4 |   0   1   1   1   1   0    1    0    0    1 |   0   0   0   0    0    1    1    0    0    1    0    0    1    0 |   *   *   *   *   *   *   *   *   *  *    *    * 1920    *    * |  0  0  1  0  0    1
sefa( s 2 s3s4s ) |    4 |   1   1   1   0   0   1    0    0    1    1 |   0   0   0   0    0    0    0    1    1    1    0    0    0    1 |   *   *   *   *   *   *   *   *   *  *    *    *    * 1920    * |  0  0  0  1  0    1
sefa( . s3s3s4s ) |    4 |   0   0   0   1   1   1    0    1    1    1 |   0   0   0   0    0    0    0    0    0    0    1    1    1    1 |   *   *   *   *   *   *   *   *   *  *    *    *    *    * 1920 |  0  0  0  0  1    1
------------------+------+---------------------------------------------+-------------------------------------------------------------------+-----------------------------------------------------------------+--------------------
      s3s3s3s .   |   60 |  30  30   0  30   0   0   60   60   60    0 |  20  20  20   0   60   60    0   60    0    0   60    0    0    0 |   5  10   0  10   0   0   5   0   0  0   60    0    0    0    0 | 32  *  *  *  *    *  snip
      s3s3s 2 s   |   24 |  12   0  12   0  12  12   24   24    0    0 |   8   8   0   0   24    0   24    0   24    0    0   24    0    0 |   2   0   4   0   6   0   0   4   0  0    0   24    0    0    0 |  * 80  *  *  *    *  snittap
      s3s 2 s4s   |   24 |   0  12  12  12  12   0   24    0    0   24 |   8   0   0   6    0   24   24    0    0   24    0    0   24    0 |   0   4   4   0   0   3   0   0   3  0    0    0   24    0    0 |  *  * 80  *  *    *  3-4-dap
      s 2 s3s4s   |   48 |  24  24  24   0   0  24    0    0   48   48 |   0   0  16  12    0    0    0   48   48   48    0    0    0   48 |   0   0   0   8  12   6   0   0   0  2    0    0    0   48    0 |  *  *  * 40  *    *  sniccap
      . s3s3s4s   |  192 |   0   0   0  96  96  96    0  192  192  192 |   0  64  64  48    0    0    0    0    0    0  192  192  192  192 |   0   0   0   0   0   0  16  32  24  8    0    0    0    0  192 |  *  *  *  * 10    *  snet
sefa( s3s3s3s4s ) |    5 |   1   1   1   1   1   1    1    1    1    1 |   0   0   0   0    1    1    1    1    1    1    1    1    1    1 |   0   0   0   0   0   0   0   0   0  0    1    1    1    1    1 |  *  *  *  *  * 1920  pen variant

starting figure: x3x3x3x4x

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