User:Fropuff/Draft 11
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This is a table of properties of the five Platonic solids.
| Name | Tetrahedron | Hexahedron or Cube |
Octahedron | Dodecahedron | Icosahedron |
|---|---|---|---|---|---|
| Picture |  |
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| Schläfli symbol | {3, 3} | {4, 3} | {3, 4} | {5, 3} | {3, 5} |
| Face polygon | triangle | square | triangle | pentagon | triangle |
| Vertex figure | triangle | triangle | square | triangle | pentagon |
| Vertices | 4 | 8 | 6 | 20 | 12 |
| Edges | 6 | 12 | 12 | 30 | 30 |
| Faces | 4 | 6 | 8 | 12 | 20 |
| Euler characteristic | 2 | 2 | 2 | 2 | 2 |
| Vertex configuration | 3.3.3 | 4.4.4 | 3.3.3.3 | 5.5.5 | 3.3.3.3.3 |
| Wythoff symbol | 3 | 3 2 | 3 | 4 2 | 4 | 3 2 | 3 | 5 2 | 5 | 3 2 |
| Dual polyhedron | tetrahedron | octahedron | cube | icosahedron | dodecahedron |
| Rotational symmetries | 12 | 24 | 60 | ||
| Symmetries | 24 | 48 | 120 | ||
| Symmetry group | Td | Oh | Ih | ||
| Angular deficiency (δ) |  |
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| Dihedral angle (θ) | ≈ 70.53° | 90° | ≈ 109.47° | ≈ 116.56° | ≈ 138.19° |
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| Solid angle (Ω) | ≈ 0.551286 | ≈ 1.57080 | ≈ 1.35935 | ≈ 2.96174 | ≈ 2.63455 |
| Standard vertex coordinates | (1,1,−1) (1,−1,1) (−1,1,1) (−1,−1,−1) |
(±1,±1,±1) | (±1,0,0) (0,±1,0) (0,0,±1) |
(±1,±1,±1) (0,±1/φ,±φ) (±1/φ,±φ,0) (±φ,0,±1/φ) |
(0,±1,±φ) (±1,±φ,0) (±φ,0,±1) |
| Edge length (a) |  |
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| Circumradius (R) |  |
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| Midradius (ρ) | |
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| Inradius (r) |  |
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| Surface area |  |
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| Volume |  |
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