Acronym sphihix Name small prismatohecatonicosahecatonicosahexacosachoron Circumradius sqrt[17+6 sqrt(5)] = 5.515107 Colonel of regiment pirshi Externallinks

As abstract polytope sphihix is isomorphic to giphihix, thereby interchanging the roles of pentagons and pentagrams, resp. replacing stip by pip and ti by tiggy.

Incidence matrix according to Dynkin symbol

```x3x3x5/3o5*b

. . .   .    | 7200 |    1    2    2 |    2    2    2    1    1 |   2   1   1   1
-------------+------+----------------+--------------------------+----------------
x . .   .    |    2 | 3600    *    * |    2    2    0    0    0 |   2   1   1   0
. x .   .    |    2 |    * 7200    * |    1    0    1    1    0 |   1   1   0   1
. . x   .    |    2 |    *    * 7200 |    0    1    1    0    1 |   1   0   1   1
-------------+------+----------------+--------------------------+----------------
x3x .   .    |    6 |    3    3    0 | 2400    *    *    *    * |   1   1   0   0
x . x   .    |    4 |    2    0    2 |    * 3600    *    *    * |   1   0   1   0
. x3x   .    |    6 |    0    3    3 |    *    * 2400    *    * |   1   0   0   1
. x .   o5*b |    5 |    0    5    0 |    *    *    * 1440    * |   0   1   0   1
. . x5/3o    |    5 |    0    0    5 |    *    *    *    * 1440 |   0   0   1   1
-------------+------+----------------+--------------------------+----------------
x3x3x   .    ♦   24 |   12   12   12 |    4    6    4    0    0 | 600   *   *   *
x3x .   o5*b ♦   60 |   30   60    0 |   20    0    0   12    0 |   * 120   *   *
x . x5/3o    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
. x3x5/3o5*b ♦   60 |    0   60   60 |    0    0   20   12   12 |   *   *   * 120
```

```x3x3x5/2o5/4*b

. . .   .      | 7200 |    1    2    2 |    2    2    2    1    1 |   2   1   1   1
---------------+------+----------------+--------------------------+----------------
x . .   .      |    2 | 3600    *    * |    2    2    0    0    0 |   2   1   1   0
. x .   .      |    2 |    * 7200    * |    1    0    1    1    0 |   1   1   0   1
. . x   .      |    2 |    *    * 7200 |    0    1    1    0    1 |   1   0   1   1
---------------+------+----------------+--------------------------+----------------
x3x .   .      |    6 |    3    3    0 | 2400    *    *    *    * |   1   1   0   0
x . x   .      |    4 |    2    0    2 |    * 3600    *    *    * |   1   0   1   0
. x3x   .      |    6 |    0    3    3 |    *    * 2400    *    * |   1   0   0   1
. x .   o5/4*b |    5 |    0    5    0 |    *    *    * 1440    * |   0   1   0   1
. . x5/2o      |    5 |    0    0    5 |    *    *    *    * 1440 |   0   0   1   1
---------------+------+----------------+--------------------------+----------------
x3x3x   .      ♦   24 |   12   12   12 |    4    6    4    0    0 | 600   *   *   *
x3x .   o5/4*b ♦   60 |   30   60    0 |   20    0    0   12    0 |   * 120   *   *
x . x5/2o      ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
. x3x5/2o5/4*b ♦   60 |    0   60   60 |    0    0   20   12   12 |   *   *   * 120
```