Great rhombihexacron
In geometry, the great rhombihexacron (or great dipteral disdodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great rhombihexahedron (U21).[1] It has 24 identical bow-tie-shaped faces, 18 vertices, and 48 edges.[2]
Great rhombihexacron | |
---|---|
Type | Star polyhedron |
Face | |
Elements | F = 24, E = 48 V = 18 (χ = −6) |
Symmetry group | Oh, [4,3], *432 |
Index references | DU21 |
dual polyhedron | Great rhombihexahedron |
It has 12 outer vertices which have the same vertex arrangement as the cuboctahedron, and 6 inner vertices with the vertex arrangement of an octahedron.
As a surface geometry, it can be seen as visually similar to a Catalan solid, the disdyakis dodecahedron, with much taller rhombus-based pyramids joined to each face of a rhombic dodecahedron.
Proportions
Each bow-tie has two angles of and two angles of . The diagonals of each bow-tie intersect at an angle of . The dihedral angle equals . The ratio between the lengths of the long edges and the short ones equals .
Notes
- Weisstein, Eric W. "Great rhombihexacron". MathWorld.
- Great Rhombihexacron—Bulatov Abstract Creations
References
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
- uniform polyhedra and duals