Question

Find the number of faces, edges and vertices of the following polyhedrons and verify them ysing Euler's Formula.

(i) Tetrahedron
(ii) Octahedron

Answer 1

Answer:

Let's begin by introducing the protagonist of this story — Euler's formula:

V - E + F = 2.

Simple though it may look, this little formula encapsulates a fundamental property of those three-dimensional solids we call polyhedra, which have fascinated mathematicians for over 4000 years. Actually I can go further and say that Euler's formula tells us something very deep about shape and space. The formula bears the name of the famous Swiss mathematician Leonhard Euler (1707 - 1783), who would have celebrated his 300th birthday this year.

What is a polyhedron?

Before we examine what Euler's formula tells us, let's look at polyhedra in a bit more detail. A polyhedron is a solid object whose surface is made up of a number of flat faces which themselves are bordered by straight lines. Each face is in fact a polygon, a closed shape in the flat 2-dimensional plane made up of points joined by straight lines.

Three polygons

its will help you

Answer 2

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(i) Tetrahedron

Number of faces = 5

Number of vertices = 6

Number of edges = 9

Clearly, F + V = E + 2i.e., 5 + 6 = 9 + 2

(ii) Octahedron

Number of faces = 8

Number of vertices = 6

Number of edges = 12

Clearly, F + V = E + 2i.e., 8 + 6 = 12 + 2