Advertisements
Advertisements
Question
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
Advertisements
Solution
Given, Vertices = 9, Faces = 9 and Edges = 16
Using Euler’s formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices and E = edges]
⇒ 9 + 9 – 16 = 2
⇒ 18 – 16 = 2
⇒ 2 = 2
Hence, the given values satisfies the Euler’s formula.
So, a polyhedron can have V = F = 9 and E = 16
Thus, we can draw a octagonal pyramid.
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 ______.
Euler’s formula is true for all three-dimensional shapes.
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 q in the following table.
| Faces | 6 |
| Vertices | q |
| Edges | 12 |
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
A solid has forty faces and sixty edges. Find the number of vertices of the solid.
