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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.
Printable version; In other projects ... Great rhombic triacontahedron ... Dover edition, ISBN 0-486-61480-8 (Table I: Regular Polytopes, (i) The nine regular ...
Print/export Download as PDF; ... This table shows a summary of regular polytope counts by dimension. ... Rhombic triacontahedron; Triakis icosahedron;
It is a stellation of the rhombic triacontahedron, and can also be called small stellated triacontahedron. Its dual is the dodecadodecahedron . Its 24 vertices are all on the 12 axes with 5-fold symmetry (i.e. each corresponds to one of the 12 vertices of the icosahedron ).
Original file (SVG file, nominally 560 × 620 pixels, file size: 21 KB) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
In geometry, the great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron. It is the dual of the great icosidodecahedron (U54). Like the convex rhombic triacontahedron it has 30 rhombic faces, 60 edges and 32 vertices (also 20 on 3-fold and 12 on 5-fold axes).
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