Icosahedron (3D) — free printable diagram

How many faces, edges and vertices an icosahedron has

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

Solid

Icosahedron

Faces

20

Edges

30

Vertices (corners)

12

Volume

V ≈ 2.182 × a³, where a is the edge length

Surface area

SA = 5√3 × a²

• All 20 faces are the same shape: an equilateral triangle.
• 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 20.
• Five triangles meet at each of the 12 vertices. It has the most faces of the five Platonic solids.
• It is the dual of the dodecahedron, and the shape of a twenty-sided die, the d20.
• 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 20 + 12 − 30 = 2.