Platonic Solids
Faces, edges, vertices, area, and volume of regular solids
About this calculator
The Platonic Solids Calculator reports the faces, edges, and vertices of each of the five regular convex polyhedra — the tetrahedron, cube, octahedron, dodecahedron, and icosahedron — and computes the surface area, volume, circumradius, inradius, midradius, and dihedral angle for any edge length. Every metric is exact, derived from the edge length with 30-digit precision, and the wireframe shows how the faces meet at each vertex. Useful for geometry, crystallography, dice design, and 3D modelling.
Common examples
- Tetrahedron, edge 1 → 4 faces, 6 edges, 4 vertices, area √3 ≈ 1.7321, volume ≈ 0.1179
- Cube, edge 2 → 6 faces, 12 edges, 8 vertices, surface area 24, volume 8
- Octahedron, edge 1 → 8 faces, 12 edges, 6 vertices, dihedral angle ≈ 109.47°
- Dodecahedron, edge 1 → 12 faces, 30 edges, 20 vertices, volume ≈ 7.6631
- Icosahedron, edge 1 → 20 faces, 30 edges, 12 vertices, area 5√3 ≈ 8.6603