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