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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 ...
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. It is also called a great strombic hexecontahedron.
Nonconvex great rhombicosidodecahedron - a nonconvex uniform polyhedron, with Schläfli symbol t 0,2 {5/3,3}. Topics referred to by the same term This disambiguation page lists articles associated with the title Great rhombicosidodecahedron .
In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, [1] great rhombicosidodecahedron, [2] [3] omnitruncated dodecahedron or omnitruncated icosahedron [4] is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.
Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of (±1/τ 2 , 0, ±τ 2 ) (±1, ±1, ± √ 5 )
It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the square faces in common), and with the great dodecicosidodecahedron (having the decagrammic faces in common).
rhombicosidodecahedron or small rhombicosidodecahedron 62: 20 triangles 30 squares 12 pentagons 120: 60: 3,4,5,4 truncated icosidodecahedron or great rhombicosidodecahedron 62: 30 squares 20 hexagons 12 decagons 180: 120: 4,6,10
(Great rhombicosidodecahedron) disdyakis triacontahedron: 2 3 5| 4.6.10 I h: U28 K33 120 180 62 30{4} + 20{6} + 12{10} 17 Snub cube: pentagonal icositetrahedron