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Question: 23 eulers theorem on polyhedra a polyhedron is a solid...

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23. [Eulers Theorem on Polyhedra] A polyhedron is a solid in three dimensions with polygonal faces and straight edges; the three-dimensional version of a polygon. A polyhedron is called a platonic solid if all of the faces are identical regular polygons. There are only five platonic solids: tetrahedron, with four triangular faces; cube, with six square faces; octahedron, with 8 triangular faces; dodecahedron, with 12 pentagonal faces; and icosahedron, with 20 triangular faces. You should look at pictures of these to help visualize.3 For each polyhedron listed below, let V be the number of vertices of the cube, let E be the number of edges, and let F be the number of faces. Calculate these values in a table along with a column for V + F. As you fill out the table, find the consistent pattern. (a) A parallelepiped. (b) A tetrahedron. (e) A dodecahedron (f) An icosahedron (g) A truncated icosahedron.4 c) A pyramid with a square base. (d) A pyramid with a hexagonal base

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