Great rhombihexacron | |
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Type | Star polyhedron |
Face |
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Elements | F = 24, E = 48 V = 18 (χ = −6) |
Symmetry group | Oh, [4,3], *432 |
Index references | DU21 |
dual polyhedron | Great rhombihexahedron |
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]
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.
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 .
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 |
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]
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.
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 .