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Q: If a polyhedron has 10 more edges than vertices how many faces does it have?

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A polyhedron has 30 edges and 12 vertices. How many faces does it have

A sphere is not a polyhedron because it has no edges, no vertices and no flat faces The word 'polyhedron' means many faces.

It has 6 vertices.

It is a triangular prism that has 5 faces, 6 vertices and 9 edges

6

eight

12 vertices A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges.

Such a polyhedron cannot exist. According to the Euler characteristics, V + F - E = 2, where V = vertices, F = faces, E = edges. This would require that the polyhedron had only two faces.

In geometry, a pentahedron is a polyhedron with five faces. That can either be a square pyramid with 5 vertices, 8 edges and 5 faces or a triangular prism with 6 vertices, 9 edges and 5 faces.

v=60-20

The only thing that can be said that there must be at least 4 faces and at least 6 edges and that the polyhedron must satisfy the Euler criterion which requires that: Faces + Vertices = Edges + 2.

If the object is a convex polyhedron, then, by Euler's characteristics, it should have 23 faces.

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