Acronym sirghi
Name small rhombated great hecatonicosachoron
Colonel of regiment (is itself locally convex – uniform polychoral members:
 by cells: did ided pip raded ti srawv hidy 120 120 0 0 120 sirghi 120 0 720 120 0
& others)
External

As abstract polytope sirghi is isomorphic to sirgashi, thereby interchanging pentagrams and pentagons, resp. replacing pip by stip. – As such sirghi is a lieutenant.

Incidence matrix according to Dynkin symbol

```x5o5/2x5o

. .   . . | 3600 |    2    4 |   1    4    2    2 |   2   2   1
----------+------+-----------+--------------------+------------
x .   . . |    2 | 3600    * |   1    2    0    0 |   2   1   0
. .   x . |    2 |    * 7200 |   0    1    1    1 |   1   1   1
----------+------+-----------+--------------------+------------
x5o   . . |    5 |    5    0 | 720    *    *    * |   2   0   0
x .   x . |    4 |    2    2 |   * 3600    *    * |   1   1   0
. o5/2x . |    5 |    0    5 |   *    * 1440    * |   1   0   1
. .   x5o |    5 |    0    5 |   *    *    * 1440 |   0   1   1
----------+------+-----------+--------------------+------------
x5o5/2x . ♦   60 |   60   60 |  12   30   12    0 | 120   *   *
x .   x5o ♦   10 |    5   10 |   0    5    0    2 |   * 720   *
. o5/2x5o ♦   30 |    0   60 |   0    0   12   12 |   *   * 120
```

```x5o5/2x5/4o

. .   .   . | 3600 |    2    4 |   1    4    2    2 |   2   2   1
------------+------+-----------+--------------------+------------
x .   .   . |    2 | 3600    * |   1    2    0    0 |   2   1   0
. .   x   . |    2 |    * 7200 |   0    1    1    1 |   1   1   1
------------+------+-----------+--------------------+------------
x5o   .   . |    5 |    5    0 | 720    *    *    * |   2   0   0
x .   x   . |    4 |    2    2 |   * 3600    *    * |   1   1   0
. o5/2x   . |    5 |    0    5 |   *    * 1440    * |   1   0   1
. .   x5/4o |    5 |    0    5 |   *    *    * 1440 |   0   1   1
------------+------+-----------+--------------------+------------
x5o5/2x   . ♦   60 |   60   60 |  12   30   12    0 | 120   *   *
x .   x5/4o ♦   10 |    5   10 |   0    5    0    2 |   * 720   *
. o5/2x5/4o ♦   30 |    0   60 |   0    0   12   12 |   *   * 120
```

```x5/4o5/3x5o

.   .   . . | 3600 |    2    4 |   1    4    2    2 |   2   2   1
------------+------+-----------+--------------------+------------
x   .   . . |    2 | 3600    * |   1    2    0    0 |   2   1   0
.   .   x . |    2 |    * 7200 |   0    1    1    1 |   1   1   1
------------+------+-----------+--------------------+------------
x5/4o   . . |    5 |    5    0 | 720    *    *    * |   2   0   0
x   .   x . |    4 |    2    2 |   * 3600    *    * |   1   1   0
.   o5/3x . |    5 |    0    5 |   *    * 1440    * |   1   0   1
.   .   x5o |    5 |    0    5 |   *    *    * 1440 |   0   1   1
------------+------+-----------+--------------------+------------
x5/4o5/3x . ♦   60 |   60   60 |  12   30   12    0 | 120   *   *
x   .   x5o ♦   10 |    5   10 |   0    5    0    2 |   * 720   *
.   o5/3x5o ♦   30 |    0   60 |   0    0   12   12 |   *   * 120
```

```x5/4o5/3x5/4o

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