Elongated dodecahedron

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Elongated dodecahedron
Rhombo-hexagonal dodecahedron.png
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
Net
Elongated dodecahedron net.png

In geometry, the elongated dodecahedron,[1] extended rhombic dodecahedron, or rhombo-hexagonal dodecahedron[2] is a convex polyhedron with 8 rhombic and 4 hexagonal faces. The hexagons can be made equilateral, or regular depending on the shape of the rhombi. 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[edit]

Part of a tessellation of space using rhombo-hexagonal dodecahedra

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 with the rhombi projected into squares.

See also[edit]

References[edit]

  1. ^ Coxeter (1973) p.257
  2. ^ Williamson (1979) p169

External links[edit]