Acronym sirghia Name small rhombated great hecatonicosachoron alterprism Circumradius sqrt([12+5 sqrt(5)]/2) = 3.404434 Confer general polytopal classes: segmentotera   scaliform

As abstract polytope sirghia is isomorphic to sirgashia, thereby interchanging pentagons and pentagrams resp. replacing pips by stips and interchanging paps with staps, as well as replacing sirghis by sirgashis and pafs by stafes.

Incidence matrix according to Dynkin symbol

```xo5ox5/2xo5ox&#x   → height = sqrt[2 sqrt(5)-4] = 0.687121
(sirghi || inv sirghi)

o.5o.5/2o.5o.    & | 7200 |    2     4     4 |    1    4    2    2     6     6 |   2    2   1    4    5    2    2 | 1   3    3
-------------------+------+------------------+---------------------------------+----------------------------------+-----------
x. ..   .. ..    & |    2 | 7200     *     * |    1    2    0    0     2     0 |   2    1   0    2    2    1    0 | 1   2    2
.. ..   x. ..    & |    2 |    * 14400     * |    0    1    1    1     0     1 |   1    1   1    1    1    0    1 | 1   2    1
oo5oo5/2oo5oo&#x   |    2 |    *     * 14400 |    0    0    0    0     2     2 |   0    0   0    2    2    1    1 | 0   2    2
-------------------+------+------------------+---------------------------------+----------------------------------+-----------
x.5o.   .. ..    & |    5 |    5     0     0 | 1440    *    *    *     *     * |   2    0   0    2    0    0    0 | 1   2    1
x. ..   x. ..    & |    4 |    2     2     0 |    * 7200    *    *     *     * |   1    1   0    0    1    0    0 | 1   1    1
.. o.5/2x. ..    & |    5 |    0     5     0 |    *    * 2880    *     *     * |   1    0   1    0    0    0    1 | 1   2    0
.. ..   x.5o.    & |    5 |    0     5     0 |    *    *    * 2880     *     * |   0    1   1    1    0    0    0 | 1   1    1
xo ..   .. ..&#x & |    3 |    1     0     2 |    *    *    *    * 14400     * |   0    0   0    1    1    1    0 | 0   1    2
.. ox   .. ..&#x & |    3 |    0     1     2 |    *    *    *    *     * 14400 |   0    0   0    1    1    0    1 | 0   2    1
-------------------+------+------------------+---------------------------------+----------------------------------+-----------
x.5o.5/2x. ..    & ♦   60 |   60    60     0 |   12   30   12    0     0     0 | 240    *   *    *    *    *    * | 1   1    0
x. ..   x.5o.    & ♦   10 |    5    10     0 |    0    5    0    2     0     0 |   * 1440   *    *    *    *    * | 1   0    1
.. o.5/2x.5o.    & ♦   30 |    0    60     0 |    0    0   12   12     0     0 |   *    * 240    *    *    *    * | 1   1    0
xo5ox   .. ..&#x & ♦   10 |    5     5    10 |    1    0    0    1     5     5 |   *    *   * 2880    *    *    * | 0   1    1
xo ..   xo ..&#x & ♦    5 |    2     2     4 |    0    1    0    0     2     2 |   *    *   *    * 7200    *    * | 0   1    1
xo ..   .. ox&#x   ♦    4 |    2     0     4 |    0    0    0    0     4     0 |   *    *   *    *    * 3600    * | 0   0    2
.. ox5/2xo ..&#x   ♦   10 |    0    10    10 |    0    0    2    0     0    10 |   *    *   *    *    *    * 1440 | 0   2    0
-------------------+------+------------------+---------------------------------+----------------------------------+-----------
x.5o.5/2x.5o.    & ♦ 3600 | 3600  7200     0 |  720 3600 1440 1440     0     0 | 120  720 120    0    0    0    0 | 2   *    *
xo5ox5/2xo ..&#x & ♦   90 |   60   120   120 |   12   30   24   12    60   120 |   1    0   1   12   30    0   12 | * 240    *
xo5ox   .. ox&#x & ♦   15 |   10    10    20 |    1    5    0    2    20    10 |   0    1   0    2    5    5    0 | *   * 1440
```