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Platonic Solids

5 4 The tetrahedron is composed of four equilateral triangles, with three meeting at every vertex. Its vertices can also be defined by the centres of four touching spheres lower right opposite. Plato associated its form with the element of Fire because of the penetrating acuteness of its edges and vertices, and because it is the simplest and most fundamental of the regular solids. The Greeks also knew the tetrahedron as puramis, whence the word pyramid. Curiously the Greek word for fire is pur. The tetrahedron has three 2fold axes, passing through the midpoints of its edges, and four 3fold axes, each passing through one vertex and the centre of the opposite face below. Any polyhedron with these axes of rotation has tetrahedral symmetry. Each Platonic Solid is contained by its circumsphere, which just touches every vertex. The Solids also define two more spheres their midsphere, which passes through the midpoint of every edge, and their insphere, which is contained by the solid, perfectly touching the centre of every face. For the tetrahedron the inradius is one third of the circumradius lower left opposite. the tetrahedron 4 faces 6 edges 4 vertices
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