Acronym pirgaghi
Name prismatorhombated great grand hecatonicosachoron
Colonel of regiment (is itself locally convex – uniform polychoral members:
 by cells: hip ided pip raded tiggy toe pirgaghi 1200 0 720 720 120 0 giphihix 0 120 720 0 120 600
& others)
External

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

Incidence matrix according to Dynkin symbol

```x3x5/2o5x

. .   . . | 7200 |    1    2    2 |    2    2    1    2    1 |   1    2   1   1
----------+------+----------------+--------------------------+-----------------
x .   . . |    2 | 3600    *    * |    2    2    0    0    0 |   1    2   1   0
. x   . . |    2 |    * 7200    * |    1    0    1    1    0 |   1    1   0   1
. .   . x |    2 |    *    * 7200 |    0    1    0    1    1 |   0    1   1   1
----------+------+----------------+--------------------------+-----------------
x3x   . . |    6 |    3    3    0 | 2400    *    *    *    * |   1    1   0   0
x .   . x |    4 |    2    0    2 |    * 3600    *    *    * |   0    1   1   0
. x5/2o . |    5 |    0    5    0 |    *    * 1440    *    * |   1    0   0   1
. x   . x |    4 |    0    2    2 |    *    *    * 3600    * |   0    1   0   1
. .   o5x |    5 |    0    0    5 |    *    *    *    * 1440 |   0    0   1   1
----------+------+----------------+--------------------------+-----------------
x3x5/2o . ♦   60 |   30   60    0 |   20    0   12    0    0 | 120    *   *   *
x3x   . x ♦   12 |    6    6    6 |    2    3    0    3    0 |   * 1200   *   *
x .   o5x ♦   10 |    5    0   10 |    0    5    0    0    2 |   *    * 720   *
. x5/2o5x ♦   60 |    0   60   60 |    0    0   12   30   12 |   *    *   * 120
```

```x3x5/3o5/4x

. .   .   . | 7200 |    1    2    2 |    2    2    1    2    1 |   1    2   1   1
------------+------+----------------+--------------------------+-----------------
x .   .   . |    2 | 3600    *    * |    2    2    0    0    0 |   1    2   1   0
. x   .   . |    2 |    * 7200    * |    1    0    1    1    0 |   1    1   0   1
. .   .   x |    2 |    *    * 7200 |    0    1    0    1    1 |   0    1   1   1
------------+------+----------------+--------------------------+-----------------
x3x   .   . |    6 |    3    3    0 | 2400    *    *    *    * |   1    1   0   0
x .   .   x |    4 |    2    0    2 |    * 3600    *    *    * |   0    1   1   0
. x5/3o   . |    5 |    0    5    0 |    *    * 1440    *    * |   1    0   0   1
. x   .   x |    4 |    0    2    2 |    *    *    * 3600    * |   0    1   0   1
. .   o5/4x |    5 |    0    0    5 |    *    *    *    * 1440 |   0    0   1   1
------------+------+----------------+--------------------------+-----------------
x3x5/3o   . ♦   60 |   30   60    0 |   20    0   12    0    0 | 120    *   *   *
x3x   .   x ♦   12 |    6    6    6 |    2    3    0    3    0 |   * 1200   *   *
x .   o5/4x ♦   10 |    5    0   10 |    0    5    0    0    2 |   *    * 720   *
. x5/3o5/4x ♦   60 |    0   60   60 |    0    0   12   30   12 |   *    *   * 120
```