MATHS QUERY
Vertices, Edges, Faces of 3-D Shapes & Euler’s Formula
TOC
Table of vertices, edges and faces of 3-D shapes
| Shape | No. of vertices | No. of edges | No. of faces |
|---|---|---|---|
| Cube | 8 | 12 | 6 |
| Cuboid | 8 | 12 | 6 |
| Cylinder | 0 | 2 | 3 |
| Sphere | 0 | 0 | 1 |
| Cone | 1 | 1 | 2 |
| Prism | 6 | 9 | 5 |
| Triangular pyramid | 4 | 6 | 4 |
| Quadrilateral pyramid | 5 | 8 | 5 |
Euler’s formula
Euler’s formula is used to find number of faces or number of vertices or number of edges.
Formula
Euler’s formula
\(F + V = E + 2\)
Example
So, let’s validate Euler’s formula for cube:
V = 8, E = 12, F = 6
Using Euler’s formula, F + V = E + 2
\(\therefore\), 6 + 8 = 12 + 2
14 = 14