Rhombo-hexagonal dodecahedron

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Rhombo-hexagonal dodecahedron
Type	Dodecahedron
Faces	8 rhombi 4 hexagons
Edges	28
Vertices	18
Vertex configuration	(8) 4.6.6 (8) 4.4.6 (2) 4.4.4
Symmetry group	D4h
Dual polyhedron	-
Properties	convex, Zonohedron

The rhombo-hexagonal dodecahedron is a convex polyhedron with 8 rhombic and 4 equilateral hexagonal faces.

It is also called an elongated dodecahedron and extended rhombic dodecahedron because it is related to the rhombic dodecahedron by expanding four rhombic faces of the rhombic dodecahedron into hexagons. It therefore shares many of the geometric properties of the rhombic dodecahedron:

• It can tesselate all space by translations.
• As the rhombic dodecahedron is the Wigner-Seitz cell for a body-centered cubic lattice, and the "rhombo-hexagonal dodecahedron" is an elongated rhombic dodecahdron, this shape is the Wigner-Seitz cell for certain bodycentered tetragonal lattices.

[edit] External links

• [1] Uniform space-filling using only rhombo-hexagonal dodecahedra
• VRML Model [2]

[edit] Reference

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.