Using Euler's formula, find the unknown in the table given below. Faces 8 5 x 1 Vertices x 2 6 12 Edges 12 x 3 30

According to Euler’s formula, in any polyhedron, F + V - E = 2 , where ‘ F ’ stands for the number of faces, ‘ V ’ stands for the number of vertices and ‘ E ’ stands for the number of edges. (i) Number of faces, F = 8 Number of edges, E = 12 Number of vertices, V = x 2 According to Euler’s formula in any polyhedron, ⇒ 8 + x 2 - 12 = 2 ⇒ x 2 - 4 = 2 ⇒ x 2 = 2 + 4 = 6 (ii) Number of faces, F = 5 Number of vertices, V = 6 Number of edges, E = x 3 According to Euler’s formula in any polyhedron, 5 + 6 - x 3 = 2 ⇒ 11 - x 3 = 2 ⇒ x 3 = 11 - 2 = 9 (iii) Number of faces, F = x 1 Number of edges, E = 30 Number of vertices, V = 12 According to Euler’s formula in any polyhedron, x 1 + 12 - 30 = 2 ⇒ x 1 - 18 = 2 ⇒ x 1 = 2 + 18 = 20 Faces 8 5 20 Vertices 6 6 12 Edges 12 9 30