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Icosidodecahedron information


Icosidodecahedron

(Click here for rotating model)
Type Archimedean solid
Uniform polyhedron
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Conway notation aD
Schläfli symbols r{5,3}
t1{5,3}
Wythoff symbol 2 | 3 5
Coxeter diagram
Symmetry group Ih, H3, [5,3], (*532), order 120
Rotation group I, [5,3]+, (532), order 60
Dihedral angle
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net
3D model of an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

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Icosidodecahedron

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geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces. An icosidodecahedron has 30 identical...

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Pentakis icosidodecahedron

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In geometry, the pentakis icosidodecahedron or subdivided icosahedron is a convex polyhedron with 80 triangular faces, 120 edges, and 42 vertices. It...

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Truncated icosidodecahedron

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In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, great rhombicosidodecahedron, omnitruncated dodecahedron or omnitruncated...

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Great icosidodecahedron

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In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54. It has 32 faces (20 triangles and 12 pentagrams), 60 edges...

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List of Wenninger polyhedron models

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Second stellation of icosidodecahedron Ih 49 Third stellation of icosidodecahedron Ih 50 Fourth stellation of icosidodecahedron (Compound of small stellated...

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Snub dodecahedron

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In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed...

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Expanded icosidodecahedron

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The expanded icosidodecahedron is a polyhedron, constructed as an expanded icosidodecahedron. It has 122 faces: 20 triangles, 60 squares, 12 pentagons...

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Small complex icosidodecahedron

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In geometry, the small complex icosidodecahedron is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32...

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Great inverted snub icosidodecahedron

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In geometry, the great inverted snub icosidodecahedron (or great vertisnub icosidodecahedron) is a uniform star polyhedron, indexed as U69. It is given...

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Great ditrigonal icosidodecahedron

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In geometry, the great ditrigonal icosidodecahedron (or great ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U47. It has...

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Great truncated icosidodecahedron

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geometry, the great truncated icosidodecahedron (or great quasitruncated icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron...

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Great complex icosidodecahedron

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In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12...

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Compound of dodecahedron and icosahedron

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hyperbolic tilings. This polyhedron is the first stellation of the icosidodecahedron, and given as Wenninger model index 47. The stellation facets for...

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Archimedean solid

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is 720° divided by the vertex angle defect. The cuboctahedron and icosidodecahedron are edge-uniform and are called quasi-regular. The duals of the Archimedean...

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Small ditrigonal icosidodecahedron

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In geometry, the small ditrigonal icosidodecahedron (or small ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U30. It has...

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Great icosicosidodecahedron

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In geometry, the great icosicosidodecahedron (or great icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U48. It has 52 faces...

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Great snub icosidodecahedron

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In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57. It has 92 faces (80 triangles and 12 pentagrams), 150...

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ID

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graphical and mathematical representation of a decision situation Icosidodecahedron, a uniform polyhedron Id, one of the Id, ego and super-ego psychic...

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Great retrosnub icosidodecahedron

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In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U74. It...

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Truncated rhombicosidodecahedron

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hexagons, and 60 squares. Truncated small rhombicosidodecahedron Beveled icosidodecahedron As a zonohedron, it can be constructed with all but 30 octagons as...

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10

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Archimedean solid can contain, as with the truncated dodecahedron and icosidodecahedron. There are ten regular star polychora in the fourth dimension, all...

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Great ditrigonal dodecicosidodecahedron

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the great ditrigonal dodecicosidodecahedron (or great dodekified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U42. It has 44 faces...

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Icositruncated dodecadodecahedron

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icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U45. Its convex hull is a nonuniform truncated icosidodecahedron. Cartesian...

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Small icosicosidodecahedron

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In geometry, the small icosicosidodecahedron (or small icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U31. It has 52 faces...

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List of mathematical shapes

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icosicosidodecahedron Great icosidodecahedron Great icosihemidodecahedron Great inverted snub icosidodecahedron Great retrosnub icosidodecahedron Great rhombidodecahedron...

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Platonic solid

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which is a rectification of the cube and the octahedron, and the icosidodecahedron, which is a rectification of the dodecahedron and the icosahedron...

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Table of polyhedron dihedral angles

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(-1/3) 109.471° Cuboctahedron r{3,4} (3.4.3.4) arccos (-√3/3) 125.264° Icosidodecahedron r{3,5} (3.5.3.5) arccos ⁡ ( − 1 15 75 + 30 5 ) {\displaystyle \arccos...

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