# Platonic Solids

41 40 the IcoSIdodecahedron 32 faces 60 edges 30 vertices The icosidodecahedron combines the twelve pentagonal faces of the dodecahedron with the twenty triangular faces of the icosahedron. Joining the edge midpoints of either the dodecahedron or the icosahedron traces out the quasiregular icosidodecahedron both are shown below as a stereogram pair. Its edges form six equatorial decagons, giving a radial projection of six great circles lower left opposite. The earliest known depiction of the icosidodecahedron is by Leonardo Da Vinci 14521519 and appears in Fra Luca Paciolis 14451517 De Divina Proportione. Appropriately this works main theme is the golden ratio, which is perfectly embodied by the ratio of the icosidodecahedrons edge to its circumradius. Defining the icosidodecahedron with thirty equal spheres leaves space for a large central sphere that is 5 see page 55 times as big as the others lower right opposite.