Acronym	sphiddix
Name	small prismatohecatonicosadishexacosachoron
Circumradius	sqrt[25+10 sqrt(5)] = 6.881910
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: grid sidditdid siid stip toe tut sphiddix 0 0 120 720 600 600 sixipady 120 120 0 720 0 600 & others)
Face vector	7200, 18000, 12240, 2040
Confer	general polytopal classes: Wythoffian polychora
External links

As abstract polytope sphiddix is isomorphic to giphiddix, thereby replacing pentagrams by pentagons, resp. stip by pip and siid by giid

Incidence matrix according to Dynkin symbol

     x    
   3 |    
     x    
  3 / \ 3 
   x---o  
    5/2   

x3x3x5/2o3*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 .   o3*b |    3 |    0    3    0 |    *    *    * 2400    * |   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 .   o3*b ♦   12 |    6   12    0 |    4    0    0    4    0 |   * 600   *   *
x . x5/2o    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
. x3x5/2o3*b ♦   60 |    0   60   60 |    0    0   20   20   12 |   *   *   * 120

     x     
   3 |     
     x     
  3 / \ 3/2
   x---o   
    5/3    

x3x3x5/3o3/2*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 .   o3/2*b |    3 |    0    3    0 |    *    *    * 2400    * |   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 .   o3/2*b ♦   12 |    6   12    0 |    4    0    0    4    0 |   * 600   *   *
x . x5/3o      ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
. x3x5/3o3/2*b ♦   60 |    0   60   60 |    0    0   20   20   12 |   *   *   * 120

x3x3o5β

both( . . . . ) | 7200 |    1    2    2 |    2    1    1    2    2 |   1   1   1   2
----------------+------+----------------+--------------------------+----------------
both( x . . . ) |    2 | 3600    *    * |    2    0    0    2    0 |   1   1   0   2
both( . x . . ) |    2 |    * 7200    * |    1    1    0    0    1 |   1   0   1   1
sefa( . . o5β ) |    2 |    *    * 7200 |    0    0    1    1    1 |   0   1   1   1
----------------+------+----------------+--------------------------+----------------
both( x3x . . ) |    6 |    3    3    0 | 2400    *    *    *    * |   1   0   0   1
both( . x3o . ) |    3 |    0    3    0 |    * 2400    *    *    * |   1   0   1   0
      . . o5β   ♦    5 |    0    0    5 |    *    * 1440    *    * |   0   1   1   0
sefa( x 2 o5β ) |    4 |    2    0    2 |    *    *    * 3600    * |   0   1   0   1
sefa( . x3o5β ) |    6 |    0    3    3 |    *    *    *    * 2400 |   0   0   1   1
----------------+------+----------------+--------------------------+----------------
both( x3x3o . ) ♦   12 |    6   12    0 |    4    4    0    0    0 | 600   *   *   *
      x 2 o5β   ♦   10 |    5    0   10 |    0    0    2    5    0 |   * 720   *   *
      . x3o5β   ♦   60 |    0   60   60 |    0   20   12    0   20 |   *   * 120   *
sefa( x3x3o5β ) ♦   24 |   12   12   12 |    4    0    0    6    4 |   *   *   * 600

starting figure: x3x3o5x