Acronym	sphihix
Name	small prismatohecatonicosahecatonicosahexacosachoron
Circumradius	sqrt[17+6 sqrt(5)] = 5.515107
Colonel of regiment	pirshi
Face vector	7200, 18000, 11280, 1560
Confer	general polytopal classes: Wythoffian polychora
External links

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