Visualising Solid Shapes


What is the least number of planes that can enclose a solid? Name the simplest regular polyhedron and verify Euler’s formula for it.


At least 4 planes can form to enclose a solid. Tetrahedron is the simple polyhedron. Following figure represents a simplest solid, called tetrahedron.

 A tetrahedron has:
              4 triangular faces, i.e. F = 4
              4 vertices,             i.e. V = 4
              6 edges,                i.e. E = 6
Now, substituting the values of F, V and E in Euler's formula, i.e.
                                F + V = E + 2
we have
                               4 + 4 = 6 + 2 
rightwards double arrow                            8 = 8, which is true.
       Thus, Euler's formula is verified for a tetrahedron.

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