Acronym	grohp
Name	great-rhombihexahedron prism
Cross sections	©
Circumradius	sqrt[(3-sqrt(2))/2] = 0.890446
Coordinates	((sqrt(2)-1)/2, 1/2, 1/2, 1/2)   & all permutations in all but last coord., all changes of sign
General of army	ticcup
Colonel of regiment	goccope
Face vector	48, 120, 84, 20
External links

Incidence matrix

48 |  2  2  1 |  2  2  2  2 |  2 2 1
---+----------+-------------+-------
 2 | 48  *  * |  1  1  0  1 |  1 1 1
 2 |  * 48  * |  1  0  1  1 |  1 1 1
 2 |  *  * 24 |  0  2  2  0 |  2 2 0
---+----------+-------------+-------
 4 |  2  2  0 | 24  *  *  * |  1 0 1
 4 |  2  0  2 |  * 24  *  * |  1 1 0  (at pseudo trip)
 4 |  0  2  2 |  *  * 24  * |  1 1 0  (at pseudo cube)
 8 |  4  4  0 |  *  *  * 12 |  0 1 1  {8/3}
---+----------+-------------+-------
 8 |  4  4  4 |  2  2  2  0 | 12 * *  cube
16 |  8  8  8 |  0  4  4  2 |  * 6 *  stop
24 | 24 24  0 | 12  0  0  6 |  * * 2  groh

or (only as abstract polychoron)
48 |  4  1 |  2  4  2 |  2 2 1
---+-------+----------+-------
 2 | 96  * |  1  1  1 |  1 1 1
 2 |  * 24 |  0  4  0 |  2 2 0
---+-------+----------+-------
 4 |  4  0 | 24  *  * |  1 0 1
 4 |  2  2 |  * 48  * |  1 1 0
 8 |  8  0 |  *  * 12 |  0 1 1  {8/3}
---+-------+----------+-------
 8 |  8  4 |  2  4  0 | 12 * *  cube
16 | 16  8 |  0  8  2 |  * 6 *  stop
24 | 48  0 | 12  0  6 |  * * 2  groh