In a polyhedron , id the number of vertices is 10 less than its number of edges and the number of faces is 8 less than the number of its vertices, then find its number of faces, edges and vertices.
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Answer:
30 edges, 20 vertices and 12 faces.
Step-by-step explanation:
Taking the edges, vertices and faces to be F, E and V respectively.
V = E - 10 (given)
F = V - 8 (given)
F = E - 18 (derived)
F + V - E = 2 (By Euler's Formula)
Taking them all in terms of E,
(E-18) + (E-10) - E = 2
(2E-E) + (-28) = 2
E - 28 = 2
E = 30
V = 30-10 = 20
F = 20 - 8 = 12
Hence, in the given polyhedron, there are 30 edges, 20 vertices and 12 faces.
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