If a polyhedron has #10# vertices and #15# edges, then how many faces does it have?

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Answer 1 · 2017-11-03T11:24:07

#7#

For any polyhedron:

#"Faces" + "Vertices" = "Edges" + 2#

So in our example:

#"Faces" + 10 = 15 + 2 = 17#

So:

#"Faces" = 17-10 = 7#

An example of such a polyhedron would be a cube (hexahedron) with one corner sliced off to create a small triangular face and three more edges.