what is the least number of planes that can enclose a solid? Name the simplest regular polyhedron and verify Euler's formula for it?
Answers
Answer:
The minimum or least no. of planes required to enclose a solid is 4.
The simplest regular polyhedron is the Tetrahedron. The figure attached below represents a simple regular solid called tetrahedron.
Now, in order to verify the Euler’s formula for the tetrahedron, we will first the calculate the no. of faces, vertices & edges from the figure which is as follows:
A tetrahedron has:
1) 4 triangular faces: F = 4
2) 4 vertices: V = 4
3) 6 edges: E = 6
The Euler’s formula is given as,
V + F - E = 2 ….. (i)
Taking the L.H.S of eq. (i)
= V + F – E
on substituting the values of V, F & E for the tetrahedron, we get
= 4 + 4 – 6
= 8 – 6
= 2
= R.H.S.
Thus, Euler’s formula is verified for the simplest regular polyhedron i.e., the tetrahedron .
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