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Recognised as Polyhedron

Tetrahedron

  • Platonic
  • 4 faces
  • Dual: tetrahedron

The tetrahedron is a Platonic solid with 4 faces, 6 edges and 4 vertices: 4 equilateral triangles. Its dual is the tetrahedron, and its dihedral angle is 70.529°. It is the only Platonic solid that is its own dual.

Faces, edges and vertices

Faces44 equilateral triangles
Edges6
Vertices4
Euler characteristicV − E + F = 4 − 6 + 4 = 2every convex polyhedron gives 2
FamilyPlatonicregular: identical regular faces meeting identically at every vertex
Dual polyhedrontetrahedron

Measurements at edge length 1

Volume0.117851cubic units for a unit edge
Surface area1.732051square units for a unit edge
Dihedral angle70.5288°the angle between two adjacent faces
Volume at edge 10117.8511
Surface area at edge 10173.2051
Isoperimetric ratio0.30231 for a sphere; higher means more efficiently packed

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