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The following table highlights some of the fundamental properties of the five Platonic solids including the face shape and the numbers of vertices, edges, and faces: Regular polyhedra (particularly the Platonic solids) are commonly seen in nature. For example, the icosahedral crystalline structure of iron pyrite and the tetrahedral structure of the methane molecule are shaped like Platonic solids. There are five types of convex regular polyhedra--the regular tetrahedron, cube, regular octahedron, regular dodecahedron, and regular icosahedron.

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Consider a convex regular polyhedron with Schläfli symbol \(\{m,n\}.\) This implies, based on the definition of the Schläfli symbols above, that color{Blue} \textbf{Regular Polyhedron}} &&{\color{Blue} \textbf{Face Shape}} &&{\color{Blue} \textbf{Vertices}} &&{\color{Blue} \textbf{Edges}} &&{\color{Blue} \textbf{Faces}} \\

Symmetries

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