Product of Number of Edges, Edges per Face and Faces of Regular Icosahedron

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Theorem

The product of the number of edges, edges per face and faces of a regular icosahedron is $1800$.


Proof

A regular icosahedron has:

$30$ edges

and:

$20$ faces.

Each face is a triangle, and so has $3$ edges.

Hence:

$30 \times 20 \times 3 = 1800$

$\blacksquare$


Sources