Verify Euler’s relation for each of the following: (i) A square prism (ii) A tetrahedron (iii) A triangular prism (iv) A square pyramid

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Solution

(i) A square prism F- E + V = 2 ⇒6-12+8=2 ⇒14-12=2⇒2=2 (ii) A tetrahedron F – E + V = 2 ⇒4-6+4=2 ⇒8-6=2 ⇒2=2 (iii) A triangular prism F – E + V = 2 ⇒5-9+6=2 ⇒11-9⇒2=2 (iv) A square pyramid F – E + V = 2 ⇒5-8+5=2 ⇒10-8=2 ⇒2=2

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