Icosahedron

icosahedron 1.gif (24748 bytes) Icosahedron

icosahedron

{3,5}

This polyhedron could have been placed in succession with the regular tetrahedron and the regular octahedron as it is just one step up form the octahedron. Instead of folding up four triangles to vertex as in the case with the octahedron, five triangles are folded together to from a vertex of an icosahedron.

In the following formulae ‘s’ is thee length of an edge of the polyhedron.

	Vertices : 12
	Edges : 30
	Faces : 20
	Edges per face : 3
	Edges per vertex : 4
	Sin of angle at edge : 2/3
	Surface area : 5Ö 3 S²
	Volume : 5 Ö 3 + Ö 5 S³/12
	Circumscribed radius : Ö 10+2Ö 5 S/4
	Inscribed radius : Ö 4² + 18 Ö 5 S/12