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