The Eulers Formula states that F V E 2 where F V and E re

The Euler\'s Formula states that F + V - E = 2 where F, V, and E represents the number of faces, vertices, and edges respectively. Verify that the formula holds for each of the following 3D solids by filling in the entries in the table.

Solution

(i) In case of triangular prism there are 5 faces, 9 edges and 6 vertices so E = 9 and hence F+V-E =2

(ii) In rectangular prism there are 6 faces,12 edges and 8 vertices so E = 12 and hence F+V-E =2

a prism whose bases are n-gons have n+2 faces, 3n edges, and 2n vertices.

(iii) In 5-gon prism there are 7 faces,15 edges and 10 vertices so F=7,V=10 and E = 15 and hence F+V-E =2

(iv) In 6-gon prism there are 8 faces,18 edges and 12 vertices so F=8,V=12 and E = 18 and hence F+V-E =2

(v) In 7-gon prism there are 9 faces,21 edges and 14 vertices so F=9,V=14 and E = 12 and hence F+V-E =2

(vi) In n-gons there are n+2 faces, 3n edges, and 2n vertices.