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
TypeStar polyhedron
Face
ElementsF = 24, E = 48
V = 18 (χ = 6)
Symmetry groupOh, [4,3], *432
Index referencesDU21
dual polyhedronGreat 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

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gollark: The HTCPCP methods?
gollark: Even PROXY? CONNECT? M-whatever it is?
gollark: My API has exactly one endpoint which receives a JSON enum to decide what to do.
gollark: I don't think it's technically impossible to have data in it anyway.

References

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