Rhombicosidodecahedron Calculator

Calculations at a regular (small) rhombicosidodecahedron. A slice plane through ten edges of a rhombicosidodecahedron forms a regular decagon. Its dual body is the deltoidal hexecontahedron.
Enter one value and choose the number of decimal places. Then click Calculate.

	Edge length (a):			62 faces, 120 edges, 60 vertices Faces: 20 equilateral triangles, 30 squares, 12 regular pentagons
	Surface area (A):
	Volume (V):
	Circumsphere radius (rc):
	Midsphere radius (rm):
	Surface-to-volume ratio (A/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

The rhombicosidodecahedron is an Archimedean solid. Edge length and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

Ikosi means twenty, and dodeka means twelve. Thus, an icosidodecahedron has 32 faces. The rhombuses that give the shape its name are somewhat harder to spot. The rhombicosidodecahedron is closely related to the icosidodecahedron and can be derived from either a dodecahedron or an icosahedron through further truncation and expansion operations. The dual form of the icosidodecahedron, in turn, is the rhombic triacontahedron, a shape that actually does feature rhombuses as its faces.
The rhombicosidodecahedron is one of three Archimedean solids composed of three different types of faces. The other two are the truncated cuboctahedron and the truncated icosidodecahedron. The truncated icosidodecahedron is also referred to as the great rhombicosidodecahedron, as it, too, possesses 32 faces and can be traced back to the icosidodecahedron. The designations small and great, used to distinguish between these two rhombicosidodecahedra, are based on the number of vertices found on their respective faces. In the case of this specific solid, the small rhombicosidodecahedron, the regular polygonal faces have only three, four, or five vertices.

This form does not occur in nature, for example, in crystals, unlike other regular solids. It is occasionally used in art, design, and architecture.

Last updated on 04/26/2026. Author: Jürgen Kummer

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