Solids with icosahedral symmetry

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Main article: Icosahedral symmetry

Solids with full icosahedral symmetry[edit]

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

Dodecahedron.jpg
{5,3}
Icosahedron.jpg
{3,5}

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

Truncateddodecahedron.jpg
3.10.10
Truncatedicosidodecahedron.jpg
4.6.10
Truncatedicosahedron.jpg
5.6.6
Rhombicosidodecahedron.jpg
3.4.5.4
Icosidodecahedron.jpg
3.5.3.5

Catalan solids - duals of the Archimedean solids.

Triakisicosahedron.jpg
V3.10.10
Disdyakistriacontahedron.jpg
V4.6.10
Pentakisdodecahedron.jpg
V5.6.6
Deltoidalhexecontahedron.jpg
V3.4.5.4
Rhombictriacontahedron.jpg
V3.5.3.5

Platonic solids[edit]

Name Picture Faces Edges Vertices Edges per face Faces meeting
at each vertex
dodecahedron Dodecahedron

(Animation)

12 30 20 5 3
icosahedron Icosahedron

(Animation)

20 30 12 3 5

Achiral Archimedean solids[edit]

Name picture Faces Edges Vertices Vertex configuration
icosidodecahedron
(quasi-regular: vertex- and edge-uniform)
Icosidodecahedron
(Video)
32 20 triangles
12 pentagons
60 30 3,5,3,5
truncated dodecahedron Truncated dodecahedron
(Video)
32 20 triangles
12 decagons
90 60 3,10,10
truncated icosahedron
or commonly football (soccer ball)
Truncated icosahedron
(Video)
32 12 pentagons
20 hexagons
90 60 5,6,6
rhombicosidodecahedron
or small rhombicosidodecahedron
Rhombicosidodecahedron
(Video)
62 20 triangles
30 squares
12 pentagons
120 60 3,4,5,4
truncated icosidodecahedron
or great rhombicosidodecahedron
Truncated icosidodecahedron
(Video)
62 30 squares
20 hexagons
12 decagons
180 120 4,6,10

Achiral Catalan solids[edit]

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

Kepler-Poinsot solids[edit]

Kepler-Poinsot solids.svg

Achiral nonconvex uniform polyhedra[edit]

Small ditrigonal icosidodecahedron.png Small icosicosidodecahedron.png Small dodecicosidodecahedron.png Small stellated dodecahedron.png Great dodecahedron.png Dodecadodecahedron.png Great truncated dodecahedron.png Rhombidodecadodecahedron.png Small rhombidodecahedron.png Ditrigonal dodecadodecahedron.png
Great ditrigonal dodecicosidodecahedron.png Small ditrigonal dodecicosidodecahedron.png Icosidodecadodecahedron.png Icositruncated dodecadodecahedron.png Great ditrigonal icosidodecahedron.png Great icosicosidodecahedron.png Small icosihemidodecahedron.png Small dodecicosahedron.png Small dodecahemidodecahedron.png Great stellated dodecahedron.png
Great icosahedron.png Great icosidodecahedron.png Great truncated icosahedron.png Rhombicosahedron.png Small stellated truncated dodecahedron.png Truncated dodecadodecahedron.png Great dodecicosidodecahedron.png Small dodecahemicosahedron.png Great dodecicosahedron.png Great dodecahemicosahedron.png
Great stellated truncated dodecahedron.png Uniform great rhombicosidodecahedron.png Great truncated icosidodecahedron.png Great dodecahemidodecahedron.png Great icosihemidodecahedron.png Great rhombidodecahedron.png Great dirhombicosidodecahedron.png Small snub icosicosidodecahedron.png Small retrosnub icosicosidodecahedron.png Great disnub dirhombidodecahedron.png

Chiral Archimedean and Catalan solids[edit]

Archimedean solids:

Name picture Faces Edges Vertices Vertex configuration
snub dodecahedron
or snub icosidodecahedron (2 chiral forms)
Snub dodecahedron (Ccw)
(Video)
Snub dodecahedron (Cw)
(Video)
92 80 triangles
12 pentagons
150 60 3,3,3,3,5

Catalan solids:

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

Chiral nonconvex uniform polyhedra[edit]

Snub dodecadodecahedron.png Snub icosidodecadodecahedron.png Great snub icosidodecahedron.png Inverted snub dodecadodecahedron.png Great snub dodecicosidodecahedron.png Great inverted snub icosidodecahedron.png Great retrosnub icosidodecahedron.png

See also[edit]