Solids with full icosahedral symmetry

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


{5,3}

{3,5}

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


3.10.10

4.6.10

5.6.6

3.4.5.4

3.5.3.5

Catalan solids - duals of the Archimedean solids.


V3.10.10

V4.6.10

V5.6.6

V3.4.5.4

V3.5.3.5

Platonic solids

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

(Animation)

12302053
icosahedron Icosahedron

(Animation)

20301235

Achiral Archimedean solids

Name picture Faces Edges Vertices Vertex configuration
icosidodecahedron
(quasi-regular: vertex- and edge-uniform)
Icosidodecahedron
(Video)
3220 triangles
12 pentagons
6030 3,5,3,5
truncated dodecahedron Truncated dodecahedron
(Video)
3220 triangles
12 decagons
90 60 3,10,10
truncated icosahedron
or commonly football (soccer ball)
Truncated icosahedron
(Video)
3212 pentagons
20 hexagons
90 60 5,6,6
rhombicosidodecahedron
or small rhombicosidodecahedron
Rhombicosidodecahedron
(Video)
6220 triangles
30 squares
12 pentagons
120603,4,5,4
truncated icosidodecahedron
or great rhombicosidodecahedron
Truncated icosidodecahedron
(Video)
6230 squares
20 hexagons
12 decagons
1801204,6,10

Achiral Catalan solids

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

Achiral nonconvex uniform polyhedra

Chiral Archimedean and Catalan solids

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)
9280 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

See also

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