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, parallelohedron
Net

In geometry, the elongated dodecahedron,[1] extended rhombic dodecahedron, rhombo-hexagonal dodecahedron[2] or hexarhombic dodecahedron[3] is a convex dodecahedron 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

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.

Variations

The elongated dodecahedron can be constructed as a contraction of a uniform truncated octahedron, where square faces are reduced to single edges and regular hexagonal faces are reduced to 60 degree rhombic faces (or pairs of equilateral triangles). This construction alternates square and rhombi on the 4-valence vertices, and has half the symmetry, D2h symmetry, order 8.


Contracted truncated octahedron
Net
Honeycomb

See also

References

  1. ↑ Coxeter (1973) p.257
  2. ↑ Williamson (1979) p169
  3. ↑ http://www.matha.mathematik.uni-dortmund.de/~thilo/contents/fedorov.htm

External links

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