| Small rhombidodecacron | |
|---|---|
 | |
| Type | Star polyhedron |
| Face |  |
| Elements | F = 60, E = 120 V = 42 (χ = −18) |
| Symmetry group | Ih, [5,3], *532 |
| Index references | DU 39 |
| dual polyhedron | Small rhombidodecahedron |
In geometry, the small rhombidodecacron is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron. It is visually identical to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces.
Each face has two angles of and two angles of . The diagonals of each antiparallelogram intersect at an angle of . The ratio between the lengths of the long edges and the short ones equals , which is the golden ratio. The dihedral angle equals .
In geometry, the small dodecicosidodecahedron (or small dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U33. It has 44 faces (12 triangles, 20 pentagons, and 12 decagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.
In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices.
In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57. It has 92 faces (80 triangles and 12 pentagrams), 150 edges, and 60 vertices. It can be represented by a Schläfli symbol sr{5⁄2,3}, and Coxeter-Dynkin diagram
In geometry, the great dodecicosacron (or great dipteral trisicosahedron) is the dual of the great dodecicosahedron (U63). It has 60 intersecting bow-tie-shaped faces.
In geometry, the medial rhombic triacontahedron is a nonconvex isohedral polyhedron. It is a stellation of the rhombic triacontahedron, and can also be called small stellated triacontahedron. Its dual is the dodecadodecahedron.
In geometry, the small rhombihexacron is the dual of the small rhombihexahedron. It is visually identical to the small hexacronic icositetrahedron. Its faces are antiparallelograms formed by pairs of coplanar triangles.
In geometry, the small hexacronic icositetrahedron is the dual of the small cubicuboctahedron. It is visually identical to the small rhombihexacron. A part of each dart lies inside the solid, hence is invisible in solid models.
In geometry, the small dodecicosacron is the dual of the small dodecicosahedron (U50). It is visually identical to the Small ditrigonal dodecacronic hexecontahedron. It has 60 intersecting bow-tie-shaped faces.
In geometry, the rhombicosacron is a nonconvex isohedral polyhedron. It is the dual of the uniform rhombicosahedron, U56. It has 50 vertices, 120 edges, and 60 crossed-quadrilateral faces.
In geometry, the great triakis octahedron is the dual of the stellated truncated hexahedron (U19). It has 24 intersecting isosceles triangle faces. Part of each triangle lies within the solid, hence is invisible in solid models.
In geometry, the great rhombihexacron (or great dipteral disdodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great rhombihexahedron (U21). It has 24 identical bow-tie-shaped faces, 18 vertices, and 48 edges.
In geometry, the small stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces.
In geometry, the medial deltoidal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the rhombidodecadodecahedron. Its 60 intersecting quadrilateral faces are kites.
In geometry, the great stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great icosahedron. It has 60 intersecting triangular faces.
In geometry, the great deltoidal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the nonconvex great rhombicosidodecahedron. It is visually identical to the great rhombidodecacron. It has 60 intersecting cross quadrilateral faces, 120 edges, and 62 vertices. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.
In geometry, the great rhombidodecacron is a nonconvex isohedral polyhedron. It is the dual of the great rhombidodecahedron. It is visually identical to the great deltoidal hexecontahedron. Its faces are antiparallelograms.
In geometry, the small icosacronic hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform small icosicosidodecahedron. Its faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models.
In geometry, the small ditrigonal dodecacronic hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform small ditrigonal dodecicosidodecahedron. It is visually identical to the small dodecicosacron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.
In geometry, the great pentakis dodecahedron is a nonconvex isohedral polyhedron.
In geometry, the great dodecacronic hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great dodecicosidodecahedron. Its 60 intersecting quadrilateral faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models.
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