# Platonic Solids

9 8 The icosahedron is composed of twenty equilateral triangles, five to a vertex. It has fifteen 2fold axes, ten 3fold axes and six 5fold axes below, known as icosahedral symmetry. When the tetrahedron, octahedron and icosahedron are made of identical triangles, the icosahedron is the largest. This led Plato to associate the icosahedron with Water, the densest and least penetrating of the three fluid elements Fire, Air and Water. The angle where two faces of a polyhedron meet at an edge is known as a dihedral angle. The icosahedron is the Platonic Solid with the largest dihedral angles. If you join the two ends of an icosahedrons edge to the centre of the solid an isosceles triangle is defined the same as the triangles that make up the faces of the Great Pyramid at Giza. Opposing edges of an icosahedron form golden rectangles see page 22. Arranging twelve equal spheres to define an icosahedron leaves space at the centre for another sphere just over nine tenths as wide as the others lower right opposite. the IcoSahedron 20 faces 30 edges 12 vertices