Acronym	thahp
Name	tetrahemihexahedral prism, vertex figure of rhohid
Cross sections	© ©
Circumradius	sqrt(3)/2 = 0.866025
Coordinates	(1/sqrt(2), 0, 0, 1/2)   & all permutations in all but last coord., all changes of sign
Dihedral angles	at {4} between cube and thah:   90° at {3} between thah and trip:   90° at {4} between cube and trip:   arccos[1/sqrt(3)] = 54.735610°
Colonel of regiment	ope
Face vector	12, 30, 26, 9
Confer	Grünbaumian relatives: 2thahp
External links

Incidence matrix

12 |  4 1 | 2 2  4 | 2 1 2
---+------+--------+------
 2 | 24 * | 1 1  1 | 1 1 1
 2 |  * 6 | 0 0  4 | 2 0 2
---+------+--------+------
 3 |  3 0 | 8 *  * | 0 1 1
 4 |  4 0 | * 6  * | 1 1 0
 4 |  2 2 | * * 12 | 1 0 1
---+------+--------+------
 8 |  8 4 | 0 2  4 | 3 * *  cube
 6 | 12 0 | 4 3  0 | * 2 *  thah
 6 |  6 3 | 2 0  3 | * * 4  trip

thah || thah   → height = 1

6 * |  4 1  0 | 2 2  4 0 0 | 1 2 2 0
* 6 |  0 1  4 | 0 0  4 2 2 | 0 2 2 1
----+---------+------------+--------
2 0 | 12 *  * | 1 1  1 0 0 | 1 1 1 0
1 1 |  * 6  * | 0 0  4 0 0 | 0 2 2 0
0 2 |  * * 12 | 0 0  1 1 1 | 0 1 1 1
----+---------+------------+--------
3 0 |  3 0  0 | 4 *  * * * | 1 1 0 0
4 0 |  4 0  0 | * 3  * * * | 1 0 1 0
2 2 |  1 2  1 | * * 12 * * | 0 1 1 0
0 3 |  0 0  3 | * *  * 4 * | 0 1 0 1
0 4 |  0 0  4 | * *  * * 3 | 0 0 1 1
----+---------+------------+--------
6 0 | 12 0  0 | 4 3  0 0 0 | 1 * * *  thah
3 3 |  3 3  3 | 1 0  3 1 0 | * 4 * *  trip
4 4 |  4 4  4 | 0 1  4 0 1 | * * 3 *  cube
0 6 |  0 0 12 | 0 0  0 4 3 | * * * 1  thah