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Platonic Solids

Platonic Solids. MATH 420 Presentation: Kelly Burgess. What are they?. Convex Polyhedron (polyhedron: 3d solid with straight edges and flat faces) All faces are congruent Same number of faces meet at each vertex Named after Greek philosopher Plato who associated each with a basic "element"

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Platonic Solids

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  1. Platonic Solids MATH 420 Presentation: Kelly Burgess

  2. What are they? • Convex Polyhedron (polyhedron: 3d solid with straight edges and flat faces) • All faces are congruent • Same number of faces meet at each vertex • Named after Greek philosopher Plato who associated each with a basic "element" • Total of 5

  3. Tetrahedron: Fire • 4 vertices • 4 faces (triangles) • 6 edges • 3 faces meet at each vertex

  4. Hexahedron: Earth • 8 vertices • 6 faces (squares) • 12 edges • 3 faces meet at each vertex

  5. Octahedron: Air • 6 vertices • 8 faces (triangles) • 12 edges • 4 faces meet at each vertex

  6. Dodecahedron: Universe • 20 vertices • 12 faces (pentagons) • 30 edges • 3 faces meet at each vertex

  7. Icosahedron: Water • 12 vertices • 20 faces (triangles) • 30 edges • 5 faces meet at each vertex

  8. Relevant Equations! let V= number of vertices, E= number of edges, F=number of faces p=number of edges on each face q=number of faces meeting at each vertex V-E+F=2 (Euler) and pF=2E=qV Why are there only 5 Platonic Solids?

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