Advertisements
Advertisements
Question
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
Advertisements
Solution
By using Euler’s formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices, E = edges]
Given, Faces (F) = 20, Vertices (V) = 12
⇒ 20 + 12 – E = 2
⇒ 32 – E = 2
⇒ E = 32 – 2
⇒ E = 30
Hence, the edges of the polyhedron are 30.
APPEARS IN
RELATED QUESTIONS
Using Euler's formula, find the values of x, y, z.
| Faces | Vertices | Edges | |
| (i) | x | 15 | 20 |
| (ii) | 6 | y | 8 |
| (iii) | 14 | 26 | z |
In a solid if F = V = 5, then the number of edges in this shape is ______.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
