Question

Look at the table.

Polyhedron
Number of Faces
Number of Edges
Number of Vertices
Polyhedron 1
4
6
4
Polyhedron 2
6
12
8
Polyhedron 3
8
10
6
Polyhedron 4
12
30
20

Which polyhedron has incorrect entries for its number of faces, edges, or vertices?
Answer
Polyhedron 1
Polyhedron 2
Polyhedron 3
Polyhedron 4

Answer 1

Polyhedron 3
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8 = F
10 = E
6 = V
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The relationship among the vertices, faces, and edges of a polyhedron is one of Euler's formulas: V + F = E + 2 where V = number of vertices, F = number of faces, and E = number of edges.

In polyhedron 3, 6 + 8 = 10 +2 is not true.