A) Faces = 4, Vertices = 4, Edges = 6
B) Faces = 8, Vertices = 6, Edges = 12
C) Faces = 5, Vertices = 1, Edges = 8
D) Faces = 20, Vertices = 12, Edges = 30
Correct Answer: C
Solution :
Euler's formula for potyhedron is \[\text{F + V - E = 2}\] [a] \[\text{F = 4, V = 4, E = 6}\] \[\therefore \] F + V - E = 4 + 4 - 6 = 2, True [b] F = 8, V = 6, E = 12 \[\therefore \] F + V - E = 8 + 6 - 12 = 2, True [c] F = 5, V = 1, E = 8 \[\therefore \] F + V - E = 5 + 1 - 8 = - 2, False [d] F = 20, V = 12, E = 30 \[\therefore \] F + V - E = 20 + 12 - 30 = 2, True
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