The rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with...

It slightly resembles an inflated rhombic triacontahedron: if one replaces each face of the rhombic triacontahedron with a single vertex and four triangles...

polyhedron of index two: The medial rhombic triacontahedron is the dual of the dodecadodecahedron. It has 30 intersecting rhombic faces. It is topologically equivalent...

region of space while moving a face to another one. Other than rhombic triacontahedron, it is one of two Catalan solids that each have the property that...

stellated triacontahedron. The great rhombic triacontahedron can be constructed by expanding the size of the faces of a rhombic triacontahedron by a factor...

medial rhombic triacontahedron (or midly rhombic triacontahedron) is a nonconvex isohedral polyhedron. It is a stellation of the rhombic triacontahedron, and...

In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a special case of a parallelepiped in which all six faces...

truncated rhombic triacontahedron, constructed as a truncation of the rhombic triacontahedron. It can more accurately be called an order-5 truncated rhombic triacontahedron...

rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron. It is the dual of the great icosidodecahedron (U54). Like the convex rhombic triacontahedron...

rhombi and 30 slim. The rhombic enneacontahedron is a zonohedron with a superficial resemblance to the rhombic triacontahedron. It can also be seen as...

from a 4-cube, and a rhombic triacontahedron from a 6-cube. The rhombic icosahedron can be derived from the rhombic triacontahedron by removing a belt of...

faces. The great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron with 30 intersecting rhombic faces. The rhombic hexecontahedron...

or the rhombic triacontahedron or the rhombic dodecahedral honeycomb or the rhombic icosahedron or the rhombic hexecontahedron or the rhombic enneacontahedron...

called a pentatruncated rhombic triacontahedron, because only the (12) order-5 vertices of the rhombic triacontahedron are truncated. The dual of the chamfered...

in non-periodic spacefillings along with the rhombic triacontahedron, the rhombic icosahedron and rhombic hexahedra. There are 6,384,634 topologically...

In geometry, a rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry...

is the same. Additionally, two Catalan solids, the rhombic dodecahedron and rhombic triacontahedron, are edge-transitive, meaning their edges are symmetric...

family exist. The rhombic icosahedron is a zonohedron made up of 20 congruent rhombs. It can be derived from the rhombic triacontahedron by removing 10 middle...

of a regular dodecahedron. It is one of the stellations of the rhombic triacontahedron. It has icosahedral symmetry (Ih). The compound is a faceting of...

icosidodecahedral rhombus being his name for a rhombic triacontahedron. There are different truncations of a rhombic triacontahedron into a topological rhombicosidodecahedron:...

rhombi Rhombic dodecahedron - 12 rhombi Rhombic icosahedron - 20 rhombi Rhombic triacontahedron - 30 rhombi Rhombic hexecontahedron - 60 rhombi Rhombic enneacontahedron...

faces, 120 edges, and 42 vertices. It is a dual of the truncated rhombic triacontahedron (chamfered dodecahedron). Its name comes from a topological construction...

operation from the rhombic triacontahedron can be seen in this animation: This polyhedron can be dissected into a central rhombic triacontahedron surrounded by:...

the regular dodecahedron (the dual of the icosahedron) and the rhombic triacontahedron. Every polyhedron with icosahedral symmetry has 60 rotational (or...

solids) are again zonohedra: Kepler's rhombic dodecahedron is the dual of the cuboctahedron. The rhombic triacontahedron is the dual of the icosidodecahedron...

dodecahedron can be formed from the rhombic triacontahedron (another zonohedron, with thirty congruent golden rhombic faces) by removing or collapsing two...

of the 5-cube. A dissection is based on 10 of 30 faces of the rhombic triacontahedron. The list OEIS: A006245 defines the number of solutions as 62,...

rhombi form the faces of the rhombic triacontahedron, the two golden rhombohedra, the Bilinski dodecahedron, and the rhombic hexecontahedron. Logarithmic...

is said to be noble. Not all isozonohedra are isohedral. For example, a rhombic icosahedron is an isozonohedron but not an isohedron. A polyhedron (or...

icositetrahedron, Rhombic triacontahedron, Triakis icosahedron, Pentakis dodecahedron, Deltoidal hexecontahedron, Disdyakis triacontahedron, Pentagonal hexecontahedron...