Acronym	phap
Name	pentachoric hemiantiprism
Circumradius	1/sqrt(2) = 0.707107
Inradius wrt. pen	1/sqrt(10) = 0.316228
Inradius wrt. tho	0
Vertex figure	©
Coordinates	(1/sqrt(2), 0, 0, 0, 0)   & all permutations, all changes of sign
General of army	tac
Colonel of regiment	tac
Dihedral angles (at margins)	at tet between pen and pen:   arccos(-3/5) = 126.869898° at oct between tho and tho:   90° at tet between pen and tho:   arccos(1/sqrt(5)) = 63.434949°
Face vector	10, 40, 80, 60, 17
Confer	general polytopal classes: segmentotera
External links

Incidence matrix

10 ♦  4  4 |  6 18 |  4 16  6 | 1  5 4
---+-------+-------+----------+-------
 2 | 20  * |  3  3 |  3  6  3 | 1  3 3
 2 |  * 20 |  0  6 |  0  6  3 | 0  2 3
---+-------+-------+----------+-------
 3 |  3  0 | 20  * |  2  2  1 | 1  2 2
 3 |  1  2 |  * 60 |  0  2  1 | 0  1 2
---+-------+-------+----------+-------
 4 |  6  0 |  4  0 | 10  *  * | 1  1 0  tet
 4 |  3  3 |  1  3 |  * 40  * | 0  1 1  tet
 6 |  6  6 |  2  6 |  *  * 10 | 0  0 2  oct
---+-------+-------+----------+-------
 5 | 10  0 | 10  0 |  5  0  0 | 2  * *  pen
 5 |  6  4 |  4  6 |  1  4  0 | * 10 *  pen
 8 | 12 12 |  8 24 |  0  8  4 | *  * 5  tho

or
5 * ♦  4  4  0 |  6 12  6  0 | 4 12  6  4 0 | 1 4 4 1 0
* 5 ♦  0  4  4 |  0  6 12  6 | 0  4  6 12 4 | 0 1 4 4 1
----+----------+-------------+--------------+----------
2 0 | 10  *  * |  3  3  0  0 | 3  6  3  0 0 | 1 3 3 0 0
1 1 |  * 20  * |  0  3  3  0 | 0  3  3  3 0 | 0 1 3 1 0
0 2 |  *  * 10 |  0  0  3  3 | 0  0  3  6 3 | 0 0 3 3 1
----+----------+-------------+--------------+----------
3 0 |  3  0  0 | 10  *  *  * | 2  2  1  0 0 | 1 2 2 0 0
2 1 |  1  2  0 |  * 30  *  * | 0  2  1  0 0 | 0 1 2 0 0
1 2 |  0  2  1 |  *  * 30  * | 0  0  1  2 0 | 0 0 2 1 0
0 3 |  0  0  3 |  *  *  * 10 | 0  0  1  2 2 | 0 0 2 2 1
----+----------+-------------+--------------+----------
4 0 |  6  0  0 |  4  0  0  0 | 5  *  *  * * | 1 1 0 0 0  tet
3 1 |  3  3  0 |  1  3  0  0 | * 20  *  * * | 0 1 1 0 0  tet
3 3 |  3  6  3 |  1  3  3  1 | *  * 10  * * | 0 0 2 0 0  oct
1 3 |  0  3  3 |  0  0  3  1 | *  *  * 20 * | 0 0 1 1 0  tet
0 4 |  0  0  6 |  0  0  0  4 | *  *  *  * 5 | 0 0 0 1 1  tet
----+----------+-------------+--------------+----------
5 0 | 10  0  0 | 10  0  0  0 | 5  0  0  0 0 | 1 * * * *  pen
4 1 |  6  4  0 |  4  6  0  0 | 1  4  0  0 0 | * 5 * * *  pen
4 4 |  6 12  6 |  4 12 12  4 | 0  4  4  4 0 | * * 5 * *  tho
1 4 |  0  4  6 |  0  0  6  4 | 0  0  0  4 1 | * * * 5 *  pen
0 5 |  0  0 10 |  0  0  0 10 | 0  0  0  0 5 | * * * * 1  pen