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

As abstract polytope grohp is isomorphic to srohp, thereby replacing octagrams by octagons, respectively groh by sroh and stop by op.

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