Groh

Groh may refer to:

People

Mathematics

Great rhombihexahedron

In geometry, the great rhombihexahedron is a nonconvex uniform polyhedron, indexed as U₂₁. Its dual is the great rhombihexacron. Its vertex figure is a crossed quadrilateral.

Orthogonal projections

Filling

There is some controversy on how to colour the faces of this polyhedron. Although the common way to fill in a polygon is to just colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, the "neo filling" is sometimes used instead as a more accurate filling. In the neo filling, orientable polyhedra are filled traditionally, but non-orientable polyhedra have their faces filled with the modulo-2 method (only odd-density regions are filled in).

Related polyhedra

It shares the vertex arrangement with the convex truncated cube. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having 12 square faces in common), and with the great cubicuboctahedron (having the octagrammic faces in common).