Pictures of Platonic Solids Why only five Platonic Solids? Dodecahedron Number of faces: 12 Number of edges: 30 Number of vertices: 20 Tetrahedron Number of faces: 4 Number of edges: 6 Number of vertices: 4 Cube Number of faces: 6 Number of edges: 12 Number of vertices: 8
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Pictures of Platonic Solids Why Only Five Platonic Solids
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Pictures of Platonic Solids Why only five Platonic Solids?
DodecahedronNumber of faces: 12Number of edges: 30Number of vertices: 20
TetrahedronNumber of faces: 4Number of edges: 6Number of vertices: 4
CubeNumber of faces: 6Number of edges: 12Number of vertices: 8
The Greeks recognized that there are only five platonic solids. But why is this so? The key observation is that the interior angles of the polygons meeting at a vertex of a polyhedron add to less than 360 degrees. Tetrahedron: Three triangels at a vertex: 3*60 = 180 degreesOctahedron: Four triangles at a vertex: 4*60 = 240 degreesIcosahedron:Five triangles at a vertex: 5*60 = 300 degrees Cube: Three squares at a vertex: 3*90 = 270 degreesDodecahedron: Three pentagons at a vertex: 3*108 = 324 degrees Note: Six triangles: 6*60 = 360 degrees Four squares: 4*90 = 360 degrees Four pentagons: 4*108 = 432 degrees Three hexagons: 3*120 = 360 degrees So there are only five Platonic Solids! *) Regular means that the sides of the polygon are all the same length. Congruent means that the polygons are all the same size
Pictures of Archimedean Solids CuboctahedronNumber of faces: 14Number of edges: 24Number of vertices: 12
IcosidodecahedronNumber of faces: 32Number of edges: 60Number of vertices: 30
Truncated TetrahedronNumber of faces: 8Number of edges: 18Number of vertices: 12