Elongated dodecahedron

Elongated dodecahedron
Type	Dodecahedron
Faces	8 rhombi 4 hexagons
Edges	28
Vertices	18
Vertex configuration	(8) 4.6.6 (8) 4.4.6 (2) 4.4.4.4
Symmetry group	D4h, [4,2], (*422), order 16
Rotation group	D4, [4,2]+, (422), order 8
Dual polyhedron	-
Properties	convex, Zonohedron

In geometry, the elongated dodecahedron, extended rhombic dodecahedron, or rhombo-hexagonal dodecahedron is a convex polyhedron with 8 rhombic and 4 hexagonal faces. The hexagons may be be equilateral, but not regular. It can be seen as constructed from a rhombic dodecahedron elongated by a square prism. Along with the rhombic dodecahedron, it is a space-filling polyhedron.

Tessellation

• It can tesselate all space by translations.
• It is the Wigner-Seitz cell for certain body-centered tetragonal lattices.

This is related to the rhombic dodecahedral honeycomb with an elongation of zero. Projected normal to the elongation direction, the honeycomb looks like a square tiling.

References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. rhombo-hexagonal dodecahedron, p169
• H.S.M. Coxeter, Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 p.257

External links

• Weisstein, Eric W. "Space-filling polyhedron". MathWorld.
• Weisstein, Eric W. "Elongated dodecahedron". MathWorld.
• [1] Uniform space-filling using only rhombo-hexagonal dodecahedra
• VRML Model [2]