Nonconvex great rhombicosidodecahedron

Nonconvex great rhombicosidodecahedron
Type	Uniform star polyhedron
Elements	F = 62, E = 120 V = 60 (χ = 2)
Faces by sides	20{3}+30{4}+12{5/2}
Wythoff symbol	5/3 3 | 2
Symmetry group	Ih, [5,3], *532
Index references	U67, C84, W105
3.4.5/3.4 (Vertex figure)	Great deltoidal hexecontahedron (dual polyhedron)

In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U₆₇. It is also called the quasirhombicosidodecahedron. It is given a Schläfli symbol t_0,2{5/3,3}. Its vertex figure is a crossed quadrilateral.

This model shares the name with the convex great rhombicosidodecahedron, also known as the truncated icosidodecahedron.

Cartesian coordinates

Cartesian coordinates for the vertices of a nonconvex great rhombicosidodecahedron are all the even permutations of

(±1/τ², 0, ±(2−1/τ))

(±1, ±1/τ³, ±1)

(±1/τ, ±1/τ², ±2/τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

Related polyhedra

It shares its vertex arrangement with the truncated great dodecahedron, and with the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the great dodecicosidodecahedron (having the triangular and pentagrammic faces in common), and the great rhombidodecahedron (having the square faces in common).

Nonconvex great rhombicosidodecahedron	Great dodecicosidodecahedron	Great rhombidodecahedron
Truncated great dodecahedron	Compound of six pentagonal prisms	Compound of twelve pentagonal prisms

See also

• List of uniform polyhedra

External links

• Weisstein, Eric W., "Great rhombicosidodecahedron" from MathWorld.
• Uniform polyhedra and duals

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Polyhedron stubs Uniform polyhedra Wikimedia Foundation. 2010. Игры ⚽ Нужно сделать НИР? Kepler–Poinsot polyhedron Nonconvex great rhombicuboctahedron Look at other dictionaries: Uniform great rhombicosidodecahedron — In geometry, the uniform great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It is also called the quasirhombicosidodecahedron .This model shares the name with the convex great rhombicosidodecahedron, which is also… …   Wikipedia Rhombicosidodecahedron — The rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid. It has 20 regular triangular faces, 30 regular square faces, 12 regular pentagonal faces, 60 vertices and 120 edges.The name rhombicosidodecahedron refers to… …   Wikipedia Great dodecicosidodecahedron — In geometry, the great dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U61.It shares the vertex and edge arrangement, as well as its triangular and pentagrammic faces, with the uniform great rhombicosidodecahedron. See also * …   Wikipedia Great rhombidodecahedron — In geometry, the great rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U73.It shares the vertex and edge arrangement, as well as its square faces, with the uniform great rhombicosidodecahedron. See also * List of uniform… …   Wikipedia Truncated great dodecahedron — Type Uniform star polyhedron Elements F = 24, E = 90 V = 60 (χ = −6) Faces by sides 12{5/2}+12{10} Wythof …   Wikipedia Truncated great icosahedron — Type Uniform star polyhedron Elements F = 32, E = 90 V = 60 (χ = 2) Faces by sides 12{5/2}+20{6} Wythoff symb …   Wikipedia Great dirhombicosidodecahedron — Type Uniform star polyhedron Elements F = 124, E = 240 V = 60 (χ = −56) Faces by sides 40{3}+60{4}+24{5/2} …   Wikipedia Truncated icosidodecahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 62, E = 180, V = 120 (χ = 2) Faces by sides …   Wikipedia Kepler–Poinsot polyhedron — In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures.… …   Wikipedia Dodecadodecahedron — Type Uniform star polyhedron Elements F = 24, E = 60 V = 30 (χ = −6) Faces by sides 12{5}+12{5/2} Wythoff symbol …   Wikipedia 18+ © Academic, 2000-2025 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”