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

Theorem

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

Proof

A regular dodecahedron has:

$30$ edges

and:

$12$ faces.

Each face is a pentagon, and so has $5$ edges.

Hence:

$30 \times 12 \times 5 = 1800$

$\blacksquare$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $72$