Acronym	padohi
Name	prismatodishecatonicosachoron
Cross sections	©
Circumradius	sqrt[4+sqrt(5)] = 2.497212
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: cho gad gike ike oho raded saddid sidditdid siddy sissid stip ti trip tut scadupthix 600 120 0 0 0 120 0 0 120 120 0 0 0 0 sidipthi 0 120 120 0 0 0 120 0 0 0 0 0 0 0 sidpixathi 0 120 120 0 0 0 0 0 0 0 0 120 0 600 sid pippady 0 120 0 0 0 120 0 0 0 0 720 0 0 0 sad phiddix 0 0 0 120 600 0 0 0 0 0 0 0 0 600 sisdipthi 0 0 0 120 0 0 0 120 0 120 0 0 0 0 padohi 0 0 0 120 0 0 0 0 0 120 720 0 1200 0 & others)
Face vector	1440, 7200, 7440, 2160
Confer	related segmentochora: sissid || raded   related scaliform: prissi   decompositions: fix || padohi   general polytopal classes: Wythoffian polychora
External links

As abstract polytope padohi is isomorphic to quipdohi, thereby replacing pentagrams and pentagons, resp. replacing ike by gike, sissid by gad and stip by pip.

Chopping off all but 288 vertices results in prissi. This could be seen best from the vertex figure of padohi: vo5ox&#q, of which the vertex figure of prissi is a faceting.

If considered with according densities, then padohi can be thought of as the external blend of 1 fix + 120 sissidpies + 720 stappyps + 1200 triddips + 120 ipes. This decomposition is described as the degenerate segmentoteron ox5/2oo5oo3xx&#x.

Incidence matrix according to Dynkin symbol

x3o5o5/2x

. . .   . | 1440 |    5    5 |    5   10    5 |   1    5   5   1
----------+------+-----------+----------------+-----------------
x . .   . |    2 | 3600    * |    2    2    0 |   1    2   1   0
. . .   x |    2 |    * 3600 |    0    2    2 |   0    1   2   1
----------+------+-----------+----------------+-----------------
x3o .   . |    3 |    3    0 | 2400    *    * |   1    1   0   0
x . .   x |    4 |    2    2 |    * 3600    * |   0    1   1   0
. . o5/2x |    5 |    0    5 |    *    * 1440 |   0    0   1   1
----------+------+-----------+----------------+-----------------
x3o5o   . ♦   12 |   30    0 |   20    0    0 | 120    *   *   *
x3o .   x ♦    6 |    6    3 |    2    3    0 |   * 1200   *   *
x . o5/2x ♦   10 |    5   10 |    0    5    2 |   *    * 720   *
. o5o5/2x ♦   12 |    0   30 |    0    0   12 |   *    *   * 120

x3o5/4o5/3x

. .   .   . | 1440 |    5    5 |    5   10    5 |   1    5   5   1
------------+------+-----------+----------------+-----------------
x .   .   . |    2 | 3600    * |    2    2    0 |   1    2   1   0
. .   .   x |    2 |    * 3600 |    0    2    2 |   0    1   2   1
------------+------+-----------+----------------+-----------------
x3o   .   . |    3 |    3    0 | 2400    *    * |   1    1   0   0
x .   .   x |    4 |    2    2 |    * 3600    * |   0    1   1   0
. .   o5/3x |    5 |    0    5 |    *    * 1440 |   0    0   1   1
------------+------+-----------+----------------+-----------------
x3o5/4o   . ♦   12 |   30    0 |   20    0    0 | 120    *   *   *
x3o   .   x ♦    6 |    6    3 |    2    3    0 |   * 1200   *   *
x .   o5/3x ♦   10 |    5   10 |    0    5    2 |   *    * 720   *
. o5/4o5/3x ♦   12 |    0   30 |    0    0   12 |   *    *   * 120

x3/2o5o5/3x

.   . .   . | 1440 |    5    5 |    5   10    5 |   1    5   5   1
------------+------+-----------+----------------+-----------------
x   . .   . |    2 | 3600    * |    2    2    0 |   1    2   1   0
.   . .   x |    2 |    * 3600 |    0    2    2 |   0    1   2   1
------------+------+-----------+----------------+-----------------
x3/2o .   . |    3 |    3    0 | 2400    *    * |   1    1   0   0
x   . .   x |    4 |    2    2 |    * 3600    * |   0    1   1   0
.   . o5/3x |    5 |    0    5 |    *    * 1440 |   0    0   1   1
------------+------+-----------+----------------+-----------------
x3/2o5o   . ♦   12 |   30    0 |   20    0    0 | 120    *   *   *
x3/2o .   x ♦    6 |    6    3 |    2    3    0 |   * 1200   *   *
x   . o5/3x ♦   10 |    5   10 |    0    5    2 |   *    * 720   *
.   o5o5/3x ♦   12 |    0   30 |    0    0   12 |   *    *   * 120

x3/2o5/4o5/2x

.   .   .   . | 1440 |    5    5 |    5   10    5 |   1    5   5   1
--------------+------+-----------+----------------+-----------------
x   .   .   . |    2 | 3600    * |    2    2    0 |   1    2   1   0
.   .   .   x |    2 |    * 3600 |    0    2    2 |   0    1   2   1
--------------+------+-----------+----------------+-----------------
x3/2o   .   . |    3 |    3    0 | 2400    *    * |   1    1   0   0
x   .   .   x |    4 |    2    2 |    * 3600    * |   0    1   1   0
.   .   o5/2x |    5 |    0    5 |    *    * 1440 |   0    0   1   1
--------------+------+-----------+----------------+-----------------
x3/2o5/4o   . ♦   12 |   30    0 |   20    0    0 | 120    *   *   *
x3/2o   .   x ♦    6 |    6    3 |    2    3    0 |   * 1200   *   *
x   .   o5/2x ♦   10 |    5   10 |    0    5    2 |   *    * 720   *
.   o5/4o5/2x ♦   12 |    0   30 |    0    0   12 |   *    *   * 120