Look a little closer.

Four equal triangular faces in space. These connections help explain why the figure behaves as it does, beyond simply entering numbers into a formula.

01 / A useful relationship

It is the simplest Platonic solid by number of faces.

Its height is a√(2/3), its surface area is √3a², and its volume is a³/(6√2). The altitude reaches the centre of the opposite equilateral face.

02 / A different perspective

It is self-dual: connecting its face centres creates another tetrahedron.

A regular tetrahedron has four congruent equilateral triangular faces, six equal edges and four vertices. Three faces meet at each vertex. An arbitrary tetrahedron is not determined by one edge and is outside these calculators.

03 / A connection to explore

It satisfies Euler’s relation: 4 vertices − 6 edges + 4 faces = 2.

Use edge, height, surface area or volume to size an ideal regular tetrahedron. The edge is the shared side of its equilateral faces; the solid’s height is not the altitude within one face.

Try the idea with numbers

Open the from an edge calculator, note its outputs, then multiply each length input by two. Volume should increase by eight and surface area by four, when every relevant length is doubled. Angle inputs and dimensionless ratios remain unchanged. This scaling experiment checks the structure of the formula rather than the precision of any real measurement.

Further reading: Regular tetrahedron at Wolfram MathWorld.