Acronym	srohp
Name	small-rhombihexahedron prism
Cross sections	©
Circumradius	sqrt[(3+sqrt(2))/2] = 1.485633
Coordinates	(1+sqrt(2), 1, 1, 1)/2   & all permutations in all but last coord., all changes of sign
General of army	sircope
Colonel of regiment	sircope
Face vector	48, 120, 84, 20
External links

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

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}
---+----------+-------------+-------
 8 |  4  4  4 |  2  2  2  0 | 12 * *  cube
16 |  8  8  8 |  0  4  4  2 |  * 6 *  op
24 | 24 24  0 | 12  0  0  6 |  * * 2  sroh

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}
---+-------+----------+-------
 8 |  8  4 |  2  4  0 | 12 * *  cube
16 | 16  8 |  0  8  2 |  * 6 *  op
24 | 48  0 | 12  0  6 |  * * 2  sroh