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Platonic Solids

16 17 all thIngS In PaIrS platonic solids two by two What happens if we join the facecentres of the Platonic Solids Starting with a tetrahedron, we discover another, inverted, tetrahedron. The facecentres of a cube produce an octahedron, and an octahedron creates a cube. The icosahedron and dodecahedron likewise produce each other. Two polyhedra whose faces and vertices correspond perfectly are known as each others duals. The tetrahedron is self dual. Dual polyhedra have the same number of edges and the same symmetries. The illustrations opposite are stereogram pairs. Hold the book at arms length and place a finger vertically, midway to the page. Focus on the finger and then bring the central blurred image into focus. The image should jump into three dimensions Dual pairs of Platonic Solids can be married with their edges touching at their midpoints to give the compound polyhedra shown below. Everything in Creation has its counterpart or opposite, and the dual relationships of the Platonic Solids are a beautiful example of this principle.
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