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In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron. As a parallelohedron, the rhombic dodecahedron can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb.
The vertices with the obtuse rhombic face angles have 4 cells. The vertices with the acute rhombic face angles have 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing.
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The concave equilateral dodecahedron, called an endo-dodecahedron. [clarification needed] A cube can be divided into a pyritohedron by bisecting all the edges, and faces in alternate directions. A regular dodecahedron is an intermediate case with equal edge lengths. A rhombic dodecahedron is a degenerate case with the 6 crossedges reduced to ...
Set of Catalan solids The rhombic dodecahedron's construction, the dual polyhedron of a cuboctahedron, by Dorman Luke construction. The Catalan solids are the dual polyhedron of Archimedean solids, a set of thirteen polyhedrons with highly symmetric forms semiregular polyhedrons in which two or more polygonal of their faces are met at a vertex. [1]
This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger.. The book was written as a guide book to building polyhedra as physical models.
The rhombic dodecahedron, generated from four line segments, no two of which are parallel to a common plane. Its most symmetric form is generated by the four long diagonals of a cube. [2] It tiles space to form the rhombic dodecahedral honeycomb. The elongated dodecahedron, generated from five line segments, with two triples of coplanar segments.