Question

Find the number of faces, vertices and edges in each of these polyhedral solids and verify Euler’s formula.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Answer 1

Polyhedron	Number of faces F	Number of vertices V	Edges E	F + V	E + 2
	5	5	8	5 + 5 = 10	8 + 2 = 10
	5	6	9	5 + 6 = 11	9 + 2 = 11
	9	10	17	9 + 10 = 19	17 + 2 = 19
	8	12	18	8 + 12 = 20	18 + 2 = 20
	6	8	12	8 + 6 = 14	12 + 2 = 14
	8	12	18	8 + 12 = 20	18 + 2 = 20
	6	8	12	8 + 6 = 14	12 + 2 = 14
	7	7	12	7 + 7 = 14	12 + 2 = 14