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Solids with icosahedral symmetry

Main article: Icosahedral symmetry

Solids with full icosahedral symmetry

Platonic solids - regular polyhedra (all faces of the same type)

Archimedean solids - polyhedra with more than one polygon face type.

50px3.10.10	50px4.6.10	50px5.6.6	50px3.4.5.4	50px3.5.3.5

Catalan solids - duals of the Archimedean solids.

50pxV3.10.10	50pxV4.6.10	50pxV5.6.6	50pxV3.4.5.4	[[Image:rhombictriacontahedron.jpg	50px]]V3.5.3.5

Platonic solids

Name	Picture	Faces	Edges	Vertices
at each vertex
dodecahedron	[[Image:Dodecahedron.jpg	50px	Dodecahedron]]
12	30	20	5	3
icosahedron	50px	Icosahedron
20	30	12	3	5

Achiral Archimedean solids

Name	picture	Faces
icosidodecahedron
(quasi-regular: vertex- and edge-uniform)	50px	Icosidodecahedron
(Video)	32	20 triangles
12 pentagons	60	30
truncated dodecahedron	50px	Truncated dodecahedron
(Video)	32	20 triangles
12 decagons	90	60
truncated icosahedron
or commonly football (soccer ball)	50px	Truncated icosahedron
(Video)	32	12 pentagons
20 hexagons	90	60
rhombicosidodecahedron
or small rhombicosidodecahedron	50px	Rhombicosidodecahedron
(Video)	62	20 triangles
30 squares
12 pentagons	120	60
truncated icosidodecahedron
or great rhombicosidodecahedron	50px	Truncated icosidodecahedron
(Video)	62	30 squares
20 hexagons
12 decagons	180	120

Achiral Catalan solids

Name	picture	Dual Archimedean solid	Faces	Edges	Vertices
rhombic triacontahedron
(quasi-regular dual: face- and edge-uniform)	50px	Rhombic triacontahedron
(Video)	icosidodecahedron	30	60	32	rhombus
triakis icosahedron	50px	Triakis icosahedron
(Video)	truncated dodecahedron	60	90	32	isosceles triangle
pentakis dodecahedron	50px	Pentakis dodecahedron
(Video)	truncated icosahedron	60	90	32	isosceles triangle
deltoidal hexecontahedron	50px	Deltoidal hexecontahedron
(Video)	rhombicosidodecahedron	60	120	62	kite
disdyakis triacontahedron
or hexakis icosahedron	50px	Disdyakis triacontahedron
(Video)	truncated icosidodecahedron	120	180	62	scalene triangle

Kepler-Poinsot solids

Achiral nonconvex uniform polyhedra===

[[Image:Great stellated truncated dodecahedron.png	50px]]	[[Image:Uniform great rhombicosidodecahedron.png	50px]]	[[Image:Great truncated icosidodecahedron.png	50px]]	[[Image:Great dodecahemidodecahedron.png	50px]]	[[Image:Great icosihemidodecahedron.png	50px]]	[[Image:Great rhombidodecahedron.png	50px]]	[[Image:Great dirhombicosidodecahedron.png	50px]]	[[Image:Small snub icosicosidodecahedron.png	50px]]	[[Image:Small retrosnub icosicosidodecahedron.png	50px]]	[[Image:Great disnub dirhombidodecahedron.png	50px]]

Chiral Archimedean and Catalan solids

Archimedean solids:

Name	picture	Faces
snub dodecahedron
or snub icosidodecahedron (2 chiral forms)	50px	Snub dodecahedron (Ccw)
(Video)
50px	Snub dodecahedron (Cw)
(Video)	92	80 triangles
12 pentagons	150	60

Catalan solids:

Name	picture	Dual Archimedean solid	Faces	Edges	Vertices	Face Polygon
pentagonal hexecontahedron	50px	Pentagonal hexecontahedron (Ccw)50px	Pentagonal hexecontahedron (Cw)
(Video)(Video)	snub dodecahedron	60	50	92	irregular pentagon

Chiral nonconvex uniform polyhedra

[[Image:Snub dodecadodecahedron.png	50px]]	[[Image:Snub icosidodecadodecahedron.png	50px]]	[[Image:Great snub icosidodecahedron.png	50px]]	[[Image:Inverted snub dodecadodecahedron.png	50px]]	[[Image:Great snub dodecicosidodecahedron.png	50px]]	[[Image:Great inverted snub icosidodecahedron.png	50px]]	[[Image:Great retrosnub icosidodecahedron.png	50px]]

Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

rotational-symmetry

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