If a polyhedron has 6 faces and 12 edges, what is the number of its vertices?
8
Euler's formula for a convex polyhedron links its faces, vertices and edges: \(F + V - E = 2\), where F is the number of faces, V the number of vertices and E the number of edges.
Step 1 — Substitute \(F = 6\) and \(E = 12\): \(6 + V - 12 = 2\).
Step 2 — \(V - 6 = 2\), so \(V = 8\).
Check — a cube has 6 faces, 12 edges and 8 vertices, and \(6 + 8 - 12 = 2\) holds. A value of 12 confuses vertices with edges, while 14 and 18 do not satisfy the formula.
8 option is correct.
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