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Vertices, Edges, Faces of 3D Shapes & Euler’s Formula

Table of vertices, edges and faces of 3D shapes

ShapeNo. of verticesNo. of edgesNo. of faces
Cube8126
Cuboid8126
Cylinder023
Sphere001
Cone112
Prism695
Triangular pyramid464
Quadrilateral pyramid585

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    
∴ 6 + 8 = 12 + 2
14 = 14