In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the small rhombihexahedron is a nonconvex uniform polyhedron

Nonconvex uniform polyhedron

In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting...

, indexed as U₁₈. It has 18 faces (12 squares and 6 octagons), 48 edges, and 24 vertices. Its vertex figure

Vertex figure

In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...

 is an antiparallelogram

Antiparallelogram

An antiparallelogram is a quadrilateral in which, like a parallelogram, the pairs of nonadjacent sides are congruent, but in which two opposite sides intersect and are therefore not parallel.-Properties:Every antiparallelogram has an axis of symmetry through its crossing point...

.

Related polyhedra

This polyhedron shares the vertex arrangement

Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....

 with the stellated truncated hexahedron. It additionally shares its edge arrangement with the convex rhombicuboctahedron

Rhombicuboctahedron

In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. Note that six of the squares only share vertices with the triangles...

 (having 12 square faces in common) and with the small cubicuboctahedron

Small cubicuboctahedron

In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces , 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral.- Related polyhedra :...

 (having the octagonal faces in common).

Rhombicuboctahedron Rhombicuboctahedron In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. Note that six of the squares only share vertices with the triangles...

Small cubicuboctahedron Small cubicuboctahedron In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces , 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral.- Related polyhedra :...

Small rhombihexahedron

Stellated truncated hexahedron

It may be constructed as the exclusive or of three octagonal prism

Octagonal prism

In geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :...

s.