Dodecahedron (3D) — free printable diagram

How many faces, edges and vertices a dodecahedron has

A dodecahedron is a 3D solid with 12 faces, 30 edges and 20 vertices. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Dodecahedron

Faces

12

Edges

30

Vertices (corners)

20

Volume

V ≈ 7.663 × a³, where a is the edge length

Surface area

SA ≈ 20.646 × a²

• All 12 faces are the same shape: a regular pentagon.
• It is one of the five Platonic solids — the only five solids whose faces are all identical regular polygons with the same number of them meeting at every vertex. The complete set is the tetrahedron (4 faces), cube (6), octahedron (8), dodecahedron (12) and icosahedron (20); this is the one with 12.
• Three pentagons meet at each of the 20 vertices.
• It is the dual of the icosahedron: swap this solid's 12 faces and 20 vertices over and you get the icosahedron's 20 faces and 12 vertices.
• “Dodeca-” is Greek for twelve, so the name says how many faces it has — the same trick that names the decagon and the dodecagon in two dimensions.
• 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 12 + 20 − 30 = 2.