Platonic Solids

Faces, edges, vertices, area, and volume of regular solids

Cube (Hexahedron) · V − E + F = 2
Faces
6
Edges
12
Vertices
8
Surface area
24
Volume
8
Inradius (r)
1
Midradius (ρ)
1.4142
Circumradius (R)
1.7321
Dihedral angle
90°
Cube (Hexahedron): Wireframe of the selected Platonic solid with its faces, edges, and verticesCube (Hexahedron): Wireframe of the selected Platonic solid with its faces, edges, and verticesFaces: 6a = 2Edges: 12Vertices: 8

关于这个计算器

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.

常见示例

  • 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