Icosahedron

Definition: An icosahedron is a regular polyhedron with 20 congruent equilateral triangular faces. It is one of the five Platonic solids.

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An icosahedron is a regular polyhedron that has 20 faces. All the faces are equilateral triangles and are all congruent, that is, all the same size. It is one of the five Platonic solids.

Faces	20. Each is an equilateral triangle
Edges	30
Vertices	12

Surface area

If s is the length of any edge, then each face has an area of

Since there are 20 faces, when we multiply the above by 20 and simplify, we get the surface area of the whole object. As the formula:

If s is the length of any edge, then the volume enclosed by the icosahedron is given by the formula: