Advertisements
Advertisements
Question
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
Advertisements
Solution
By using Euler’s formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices, E = edges]
⇒ 8 + 12 – 6 = 2
⇒ 20 – 6 = 2
⇒ 14 ≠ 2
∴ Given values do not satisfy the Euler’s formula. It mean this type of polyhedron cannot be possible.
APPEARS IN
RELATED QUESTIONS
In a solid if F = V = 5, then the number of edges in this shape is ______.
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
A polyhedron can have 10 faces, 20 edges and 15 vertices.
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 z in the following table.
| Faces | 9 |
| Vertices | z |
| Edges | 16 |
Using Euler’s formula, find the value of unknown p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
