Acronym sirgashia
Name small rhombated grand stellated hecatonicosachoron alterprism
Circumradius (1+sqrt(5))/2 = 1.618034
Confer
general polytopal classes:
segmentotera   scaliform  

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


Incidence matrix according to Dynkin symbol

xo5/2ox5xo5/2ox&#x   → height = sqrt[10 sqrt(5)-22] = 0.600566
(sirgashi || inv sirgashi)

o.5/2o.5o.5/2o.    & | 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
oo5/2oo5oo5/2oo&#x   |    2 |    *     * 14400 |    0    0    0    0     2     2 |   0    0   0    2    2    1    1 | 0   2    2
---------------------+------+------------------+---------------------------------+----------------------------------+-----------
x.5/2o. ..   ..    & |    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.5x.   ..    & |    5 |    0     5     0 |    *    * 2880    *     *     * |   1    0   1    0    0    0    1 | 1   2    0
..   .. x.5/2o.    & |    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.5/2o.5x.   ..    &    60 |   60    60     0 |   12   30   12    0     0     0 | 240    *   *    *    *    *    * | 1   1    0
x.   .. x.5/2o.    &    10 |    5    10     0 |    0    5    0    2     0     0 |   * 1440   *    *    *    *    * | 1   0    1
..   o.5x.5/2o.    &    30 |    0    60     0 |    0    0   12   12     0     0 |   *    * 240    *    *    *    * | 1   1    0
xo5/2ox ..   ..&#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
..   ox5xo   ..&#x      10 |    0    10    10 |    0    0    2    0     0    10 |   *    *   *    *    *    * 1440 | 0   2    0
---------------------+------+------------------+---------------------------------+----------------------------------+-----------
x.5/2o.5x.5/2o.    &  3600 | 3600  7200     0 |  720 3600 1440 1440     0     0 | 120  720 120    0    0    0    0 | 2   *    *
xo5/2ox5xo   ..&#x &    90 |   60   120   120 |   12   30   24   12    60   120 |   1    0   1   12   30    0   12 | * 240    *
xo5/2ox ..   ox&#x &    15 |   10    10    20 |    1    5    0    2    20    10 |   0    1   0    2    5    5    0 | *   * 1440

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