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one face of this polyhedron is a pentagon. the polyhedron has a total of six vertices pentagonal pyramid a rectangular prism has dimensions 10 cm by 12 cm by 6 cm. what is the sum of the lengths of the edges
I assume that we're talking about an ordinary polyhedron that looks topologically like a sphere, not like some kind of torus or multi-sheeted sphere or whatnot. Apply Euler's Formula: VerticesâEdges+Faces = 2, for a polyhedron. Plugging in your numbers gives Vâ24+10 = 2, from which we see that V = 16. Alternative solution: Draw an octagonal prism, and confirm that your figure has 16 vertices, 10 faces, and 24 edges. Written Apr 13, 2013 Â· View Upvotes.