Elongated dodecahedron

Elongated dodecahedron
TypeParallelohedron
Faces8 rhombi
4 hexagons
Edges28
Vertices18
Vertex configuration(8) 4.6.6
(8) 4.4.6
(2) 4.4.4.4
Symmetry groupDihedral (D4h), [4,2], (*422), order 16
Rotation groupD4, [4,2]+, (422), order 8
PropertiesConvex
Net
3D model of a elongated dodecahedron
3D model of a elongated dodecahedron

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.

  1. ^ Coxeter (1973) p.257
  2. ^ Williamson (1979) p169
  3. ^ Fedorov's five parallelohedra in R³