Acronym	groh
TOCID symbol	rc|OC*
Name	great rhombihexahedron
	© ©
Circumradius	sqrt[5-2 sqrt(2)]/2 = 0.736813
Vertex figure	[4/3,8/5,4,8/3]/0
Coordinates	((sqrt(2)-1)/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army	tic
Colonel of regiment	gocco
Dihedral angles	between {4} and {8/3} (at pseudo{3}):   90° between {4} and {8/3} (at pseudo{4}):   45°
Face vector	24, 48, 18
Confer	Grünbaumian relatives: groh+8{6/2}   blend-component: stop   compounds: rasquahr
External links

As abstract polytope groh is isomorphic to sroh, thereby replacing octagrams by octagons.

This polyhedron could be thought of as the blend of 3 mutually perpendicular stop, blending out those squares at intersection axes.

This polyhedron is an edge-faceting of the great cubicuboctahedron (gocco).

The below provided matrix looks like both edge types would be alike. And in fact at each of them a square adjoins an octagram. However some are situated at a pseudo triangle (triangular hole), while the others are situated at a psuedo square (square hole). I.e. although the according symmetry equivalence classes behave alike the individual members within the full 0-1 matrix would behave differently. And therefore those remain different too within the according abstract polyhedron.

Incidence matrix according to Dynkin symbol

reduced( x4/3x3/2x , by 8{6/2} )

24 |  2  2 |  2 2
---+-------+-----
 2 | 24  * |  1 1  at pseudo {3}
 2 |  * 24 |  1 1  at pseudo {4}
---+-------+-----
 4 |  2  2 | 12 *
 8 |  4  4 |  * 6