Question 1004695: What is the relationship between the number of vertices, the number of faces and the number of edges of a triangular prism and a pyramid whose base is a regular triangle?
Answer by ikleyn(52794)   (Show Source):
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What is the relationship between the number of vertices, the number of faces and the number of edges
of a triangular prism and a pyramid whose base is a regular triangle?
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For a triangular prism: F - E + V = 5 - 9 + 6 = 2,
where F is the number of faces, E is the number of edges and V is the number of vertices.
For a triangular pyramid: F - E + V = 4 - 6 + 4 = 2,
the same number as for a triangular prism.
It is the consequence of the famous Euler's theorem.
The fact that the base is a regular triangle, is not essentially important.
The relation is valid for many polyhedra that are surfaces of convex solid bodies. See the referred Wikipedia article.
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