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[1] [2] There are different truncations of a rhombic triacontahedron into a topological rhombicosidodecahedron: Prominently its rectification (left), the one that creates the uniform solid (center), and the rectification of the dual icosidodecahedron (right), which is the core of the dual compound.
3D model of a rhombic triacontahedron. The rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron.
Great rhombic triacontahedron; Great rhombidodecacron; Great rhombihexacron; Great stellapentakis dodecahedron; Great triakis icosahedron; Great triakis octahedron; Great triambic icosahedron; Medial deltoidal hexecontahedron; Medial disdyakis triacontahedron; Medial hexagonal hexecontahedron; Medial icosacronic hexecontahedron
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Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide ... and a rhombic triacontahedron. [1] Related polyhedra
It has 30 intersecting rhombic faces. It can also be called the great stellated triacontahedron. It can also be called the great stellated triacontahedron. The great rhombic triacontahedron can be constructed by expanding the size of the faces of a rhombic triacontahedron by a factor of τ 3 = 1+2 τ = 2+√5, where τ is the golden ratio .
In geometry, the chamfered icosahedron is a convex polyhedron constructed by truncating the 20 order-3 vertices of the rhombic triacontahedron. The hexagonal faces of the cI can be made equilateral, but not regular, with a certain depth of truncation. The chamfered icosahedron can also be called a tritruncated rhombic triacontahedron.
The rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry. The rhombic enneacontahedron is a polyhedron composed of 90 rhombic faces, with three, five, or six rhombi meeting at each vertex. It has 60 broad rhombi and 30 slim ones.