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Polyhedra and Prisms
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Definitions A polyhedron is a solid, bounded by polygons (called faces), that enclose a (single) volume, or region of space. An edge is a line formed by the intersection of 2 faces. A vertex is a point where 3 or more edges come together.
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Cylinders, spheres and cones are not polyhedra. Why not?
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Prisms and Pyramids A prism has 2 bases that are congruent, and are in parallel planes. A pyramid has one base that is a polygon.
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Regular Polyhedra A Polyhedron is a regular polyhedron if all of its faces are congruent, regular polygons. A die would be an example. Would a soccer ball be one, assuming the polygons were planes?
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Convex Polyhedra A polyhedron is convex if any 2 points on its surface can be connected by a line segment within or on the surface of the polyhedron. If a polyhedron does not meet the criteria for being convex, then it would be concave.
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Euler’s Theorem F + V = E + 2 F = the number of faces
V = the number of vertices E = the number of edges
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Platonic Solids
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Tetrahedron
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Octahedron
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Dodecahedron
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Icosahedron
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