Four triangular faces, six edges, four vertices — the smallest possible polyhedron. It's the first Platonic solid, and a 'triangular pyramid' where the base is just another triangle.
Spin the solid
Tetrahedron
faces
4
4
edges
6
6
vertices
4
4
V − E + F = 4 − 6 + 4 = 2
drag to rotate
Tetrahedron at a glance
- 4 faces (equilateral triangles), 6 edges, 4 vertices — and Euler checks out: 4 − 6 + 4 = 2.
- 3 faces meet at every vertex — the minimum to make a corner.
- It's self-dual: join the centres of its faces and you get... another tetrahedron.
- Rigid and stable — which is why you see it in molecules (methane, CH₄), trusses and the universal pyramid-tent shape.
Volume from the edge length
≈ 0.118 a³ — a tetrahedron is surprisingly empty for its size.
Spin the solid above and pause it: count 4 triangles, 4 corners. Every pair of edges that doesn't share a vertex is 'skew' — they never meet, even extended.