Question

can a polyhedron have a 10 faces 12 edges and 15 verticles.

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Answer 1

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By Euler's formula for a polyhedron, Vertices (V) - Edges (E) + Faces (F) =2

Here,  

Faces (F) = 10; Vertices (V) = 12 and Edges (E) = 15

Thus,

12 - 15 + 10 = 7, which does not satisfy the Euler's formula. 

Hence,

A polyhedron can have 10 faces, 12 edges and 15 vertices

● It is a Heptahedron.