Question 1004695
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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 &nbsp;<A HREF=https://en.wikipedia.org/wiki/Euler_characteristic>Euler's theorem</A>.


The fact that the base is a regular triangle, &nbsp;is not essentially important.
The relation is valid for many polyhedra that are surfaces of convex solid bodies. &nbsp;See the referred Wikipedia article.