# The Efficient Bug

Geometry Level 4

A bug wants to walk from one vertex to the opposite vertex of an icosahedron in the most efficient way, and must stay on the surface.(i.e. At no time can it delve into the icosahedron's interior.)

The edges of the icosahedron have unit length.

If the minimum distance the bug must travel is $$x$$, what is $$x^2$$?

###### Try more questions on Platonic Solids.

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