Acronym stasissiddow
Name (pentagramm,sissid)-disphenoid,
pentagram atop fully orthogonal small stellated doedcahedron
Circumradius sqrt[(10-sqrt(5))/19] = 0.639240
Confer
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

xo5/2oo5oo ox5/2oo&#x   → height = sqrt[(9 sqrt(5)-5)/40] = 0.614911

o.5/2o.5o. o.5/2o.    | 12 * |  5  5 0 |  5  25  5 0 | 1 25  25  1 | 5 25  5 | 5  5
.o5/2.o5.o .o5/2.o    |  * 5 |  0 12 2 |  0  30 24 1 | 0 12  60 12 | 1 24 30 | 2 12
----------------------+------+---------+-------------+-------------+---------+-----
x.   .. .. ..   ..    |  2 0 | 30  * * | 10   5  0 0 | 1 10   5  0 | 5 10  1 | 5  2
oo5/2oo5oo oo5/2oo&#x |  1 1 |  * 60 * |  0   5  2 0 | 0  5  10  1 | 1 10  5 | 2  5
..   .. .. .x   ..    |  0 2 |  *  * 5 |  0   0 12 1 | 0  0  30 12 | 0 12 30 | 1 12
----------------------+------+---------+-------------+-------------+---------+-----
x.5/2o. .. ..   ..    |  5 0 |  5  0 0 | 12   *  * * | 1  5   0  0 | 5  5  0 | 5  1
xo   .. .. ..   ..&#x |  2 1 |  1  2 0 |  * 150  * * | 0  2   2  0 | 1  4  1 | 2  2
..   .. .. ox   ..&#x |  1 2 |  0  2 1 |  *   * 60 * | 0  0   5  1 | 0  5  5 | 1  5
..   .. .. .x5/2.o    |  0 5 |  0  0 5 |  *   *  * 1 | 0  0   0 12 | 0  0 30 | 0 12
----------------------+------+---------+-------------+-------------+---------+-----
x.5/2o.5o. ..   ..     12 0 | 30  0 0 | 12   0  0 0 | 1  *   *  * | 5  0  0 | 5  0
xo5/2oo .. ..   ..&#x   5 1 |  5  5 0 |  1   5  0 0 | * 60   *  * | 1  2  0 | 2  1
xo   .. .. ox   ..&#x   2 2 |  1  4 1 |  0   2  2 0 | *  * 150  * | 0  2  1 | 1  2
..   .. .. ox5/2oo&#x   1 5 |  0  5 5 |  0   0  5 1 | *  *   * 12 | 0  0  5 | 0  5
----------------------+------+---------+-------------+-------------+---------+-----
xo5/2oo5oo ..   ..&#x  12 1 | 30 12 0 | 12  30  0 0 | 1 12   0  0 | 5  *  * | 2  0
xo5/2oo .. ox   ..&#x   5 2 |  5 10 1 |  1  10  5 0 | 0  2   5  0 | * 60  * | 1  1
xo   .. .. ox5/2oo&#x   2 5 |  1 10 5 |  0   5 10 1 | 0  0   5  2 | *  * 30 | 0  2
----------------------+------+---------+-------------+-------------+---------+-----
xo5/2oo5oo ox   ..&#x  12 2 | 30 24 1 | 12  60 12 0 | 1 24  30  0 | 2 12  0 | 5  *
xo5/2oo .. ox5/2oo&#x   5 5 |  5 25 5 |  1  25 25 1 | 0  5  25  5 | 0  5  5 | * 12

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