Question

A polyhedron has 6 faces and 12 edges. How many vertices does it have?​

Answer 1

Given:-

A polyhedron has:-

• 6 faces
• 12 edges

To Find:-

• No. of vertices

Solution:-

Using Euler's Formulas i.e F + V - E = 2

➺ F + V - E = 2

➺ 6 + V - 12 = 2

➺ 6 - 12 + V = 2

➺ -6 + V = 2

➺ V = 2 + 6

∴ V = 8

Verification:-

➺ F + V - E = 2

➺ 6 + 8 - 12 = 2

➺ 14 - 12 = 2

➺ 2 = 2

LHS = RHS

Hence Verified!

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Answer 2

ANSWER

Given: Faces and edges of a polyhedron.

__________________________ To find : Vertices of the polyhedron

__________________________

Formula used: Euler's Formula

=F+V=E+2

__________________________

Let's do

6+12=edge+2

18=edge+2

18-2=edge

16=edge

__________________________

VERIFICATION

Formula used:F+V-E=2

__________________________

6+12-16=2

18-16=2

2=2

LHS=RHS