Triangular Pyramid / Tetrahedron (3D) — free printable diagram

How many faces, edges and vertices a triangular pyramid has

A triangular pyramid is a 3D solid with 4 faces, 6 edges and 4 vertices. It is also called a tetrahedron. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Triangular pyramid (tetrahedron)

Faces

4

Edges

6

Vertices (corners)

4

Shape of the base

Triangle

Triangular faces

3

Apex

1 — the single point where the triangles meet

Volume

V = ⅓ × area of the triangular base × perpendicular height

Surface area

SA = area of the base + the areas of the three triangular faces

• A pyramid has one base and a single apex above it. This one has a triangular base and 3 triangular faces rising to the apex, so 3 + 1 = 4 faces altogether.
• Every triangular pyramid has 6 edges (2 × 3: 3 around the base and 3 rising to the apex) and 4 vertices — the 3 corners of the base plus the apex.
• It is the only pyramid whose base is the same shape as its other faces, so any one of its four triangles can be treated as the base. That is also why it has the fewest faces of any polyhedron: four is the minimum.
• When all four faces are equilateral triangles it is the regular tetrahedron, one of the five Platonic solids.
• Euler's formula holds for every solid with flat faces: faces + vertices − edges = 2. It is the quickest way to check a count you are unsure of. Here that is 4 + 4 − 6 = 2.