Acronym snod (snix)
Name snub dodecateron
(snub hexateron),
alternation of great cellated hexateron
Circumradius ...
Confer
general polytopal classes:
isogonal  
External
links
polytopewiki

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

The full symmetrical variants using the outer symmetry of the Dynkin diagram is refered to as snod, while the subsymmetric variants which break its outer symmetry get refered to as snix.


Incidence matrix according to Dynkin symbol

s3s3s3s3s

demi( . . . . . )   | 360 |   2   2   1   1   4   4 |   2   2   6   6   6   6   3   3 |  2   2   2   2  1  1   8   8   4 |  2  2  1   5
--------------------+-----+-------------------------+---------------------------------+----------------------------------+-------------
      s 2 s . .   & |   2 | 360   *   *   *   *   * |   0   0   2   0   0   2   2   0 |  1   0   0   1  1  0   2   4   0 |  1  2  0   2  q
      s 2 . s .   & |   2 |   * 360   *   *   *   * |   0   0   0   2   2   2   0   0 |  0   1   1   1  0  0   2   2   2 |  1  1  1   2  q
      s . 2 . s     |   2 |   *   * 180   *   *   * |   0   0   0   0   4   0   2   0 |  0   0   2   0  1  0   0   4   2 |  0  2  1   2  q
      . s 2 s .     |   2 |   *   *   * 180   *   * |   0   0   0   4   0   0   0   2 |  0   2   0   0  0  1   4   0   2 |  2  0  1   2  q
sefa( s3s . . . ) & |   2 |   *   *   *   * 720   * |   1   0   1   1   1   0   0   0 |  1   1   1   0  0  0   1   1   1 |  1  1  1   1  h
sefa( . s3s . . ) & |   2 |   *   *   *   *   * 720 |   0   1   1   0   0   1   0   1 |  1   0   0   1  0  1   2   1   0 |  2  1  0   1  h
--------------------+-----+-------------------------+---------------------------------+----------------------------------+-------------
      s3s . . .   & |   3 |   0   0   0   0   3   0 | 240   *   *   *   *   *   *   * |  1   1   1   0  0  0   0   0   0 |  1  1  1   0  h3o
      . s3s . .   & |   3 |   0   0   0   0   0   3 |   * 240   *   *   *   *   *   * |  1   0   0   1  0  1   0   0   0 |  2  1  0   0  h3o
sefa( s3s3s . . ) & |   3 |   1   0   0   0   1   1 |   *   * 720   *   *   *   *   * |  1   0   0   0  0  0   1   1   0 |  1  1  0   1  oq&#h
sefa( s3s 2 s . ) & |   3 |   0   1   0   1   1   0 |   *   *   * 720   *   *   *   * |  0   1   0   0  0  0   1   0   1 |  1  0  1   1  oh&#q
sefa( s3s 2 . s ) & |   3 |   0   1   1   0   1   0 |   *   *   *   * 720   *   *   * |  0   0   1   0  0  0   0   1   1 |  0  1  1   1  oh&#q
sefa( s 2 s3s . ) & |   3 |   1   1   0   0   0   1 |   *   *   *   *   * 720   *   * |  0   0   0   1  0  0   1   1   0 |  1  1  0   1  oh&#q
sefa( s 2 s 2 s )   |   3 |   2   0   1   0   0   0 |   *   *   *   *   *   * 360   * |  0   0   0   0  1  0   0   2   0 |  0  2  0   1  q3o
sefa( . s3s3s . )   |   3 |   0   0   0   1   0   2 |   *   *   *   *   *   *   * 360 |  0   0   0   0  0  1   2   0   0 |  2  0  0   1  oq&#h
--------------------+-----+-------------------------+---------------------------------+----------------------------------+-------------
      s3s3s . .   & |  12 |   6   0   0   0  12  12 |   4   4  12   0   0   0   0   0 | 60   *   *   *  *  *   *   *   * |  1  1  0   0  pyritohedral ike variant
      s3s 2 s .   & |   6 |   0   3   0   3   6   0 |   2   0   0   6   0   0   0   0 |  * 120   *   *  *  *   *   *   * |  1  0  1   0  triangular antiprism
      s3s 2 . s   & |   6 |   0   3   3   0   6   0 |   2   0   0   0   6   0   0   0 |  *   * 120   *  *  *   *   *   * |  0  1  1   0  triangular antiprism
      s 2 s3s .   & |   6 |   3   3   0   0   0   6 |   0   2   0   0   0   6   0   0 |  *   *   * 120  *  *   *   *   * |  1  1  0   0  triangular antiprism
      s 2 s 2 s     |   4 |   4   0   2   0   0   0 |   0   0   0   0   0   0   4   0 |  *   *   *   * 90  *   *   *   * |  0  2  0   0  q-tetrahedra
      . s3s3s .     |  12 |   0   0   0   6   0  24 |   0   8   0   0   0   0   0  12 |  *   *   *   *  * 30   *   *   * |  2  0  0   0  pyritohedral ike variant
sefa( s3s3s3s . ) & |   4 |   1   1   0   1   1   2 |   0   0   1   1   0   1   0   1 |  *   *   *   *  *  * 720   *   * |  1  0  0   1  chiral digonal antifrustrum (disphenoid)
sefa( s3s3s 2 s ) & |   4 |   2   1   1   0   1   1 |   0   0   1   0   1   1   1   0 |  *   *   *   *  *  *   * 720   * |  0  1  0   1  pyramid above isot
sefa( s3s 2 s3s )   |   4 |   0   2   1   1   2   0 |   0   0   0   2   2   0   0   0 |  *   *   *   *  *  *   *   * 360 |  0  0  1   1  digonal antiprism
--------------------+-----+-------------------------+---------------------------------+----------------------------------+-------------
      s3s3s3s .   & |  60 |  30  30   0  30  60 120 |  20  40  60  60   0  60   0  60 |  5  10   0  10  0  5  60   0   0 | 12  *  *   *  snub decachoron
      s3s3s 2 s   & |  24 |  24  12  12   0  24  24 |   8   8  24   0  24  24  24   0 |  2   0   4   4  6  0   0  24   0 |  * 30  *   *  pyritohedral ike antiprism
      s3s 2 s3s     |  18 |   0  18   9   9  36   0 |  12   0   0  36  36   0   0   0 |  0   6   6   0  0  0   0   0  18 |  *  * 20   *  triangle duoantiprism
sefa( s3s3s3s3s )   |   5 |   2   2   1   1   2   2 |   0   0   2   2   2   2   1   1 |  0   0   0   0  0  0   2   2   1 |  *  *  * 360  pentachoron variant

starting figure: x3x3x3x3x

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