Platonic solids

Keywords: Platonic solids, also called the regular solids or regular polyhedra
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Name
Tetrahedron
Hexahedron
(Cube)
Octahedron
Dodecahedron
Icosahedron
Picture
Tetrahedron
Hexahedron (Cube)
Octahedron
Dodecahedron
Icosahedron
Net
Tetrahedron net
Hexahedron (Cube) net
Octahedron net
Dodecahedron net
Icosahedron net
Faces
4
6
8
12
20
Face type
equilateral triangle
square
equilateral triangle
equilateral pentagon
equilateral triangle
Duality
tetrahedron
octahedron
hexahedron
icosahedron
dodecahedron
Edges
6
12
12
30
30
Vertices
4
8
6
20
12
Edges from vertex
3
3
4
3
5
Number of diagonals
0
4
3
100
36
Dihedral angle
≈70°31'43,61''
90°
≈109°28'16,39''
≈116°33'55,84''
≈138°11'22,87''
Surface area
3 a 2
6 a 2
2 3 a 2
3 25 + 10 5 a 2
5 3 a 2
Volume
2 a 3 12
a 3
2 a 3 3
( 15 + 7 5 ) a 3 4
( 15 + 5 5 ) a 3 12
Circumradiu
6 a 4
3 a 2
3 a 2
3 ( 1 + 5 ) a 4
10 + 2 5 a 4
Inradiu
6 a 12
a 2
6 a 6
1 2 25 + 11 5 10 a
42 + 18 5 12 a
Midradius
2 a 4
2 a 2
a 2
( 5 + 3 ) a 4
( 1 + 5 ) a 4

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