Acronym stapepy
Name pentagram-antiprismatical pyramid
Circumradius sqrt[(25+sqrt(5))/62] = 0.662791
Face vector 11, 30, 32, 13
Confer
more general:
n-appy  
general polytopal classes:
segmentochora  

Incidence matrix

pt || stap   → height = sqrt[(25-sqrt(5))/40] = 0.569098

1  *  10  0  0 | 10 10 0  0 | 2 10 0
* 10 |  1  2  2 |  2  2 1  3 | 1  3 1
-----+----------+------------+-------
1  1 | 10  *  * |  2  2 0  0 | 1  3 0
0  2 |  * 10  * |  1  0 1  1 | 1  1 1
0  2 |  *  * 10 |  0  1 0  2 | 0  2 1
-----+----------+------------+-------
1  2 |  2  1  0 | 10  * *  * | 1  1 0
1  2 |  2  0  1 |  * 10 *  * | 0  2 0
0  5 |  0  5  0 |  *  * 2  * | 1  0 1  {5/2}
0  3 |  0  1  2 |  *  * * 10 | 0  1 1
-----+----------+------------+-------
1  5 |  5  5  0 |  5  0 1  0 | 2  * *  stappy
1  3 |  3  1  2 |  1  2 0  1 | * 10 *  tet
0 10 |  0 10 10 |  0  0 2 10 | *  * 1  stap

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