Slime Mold on a Cuboctahedron

Geometry Level 5

A slime mold, in spite of being really just a collection of single cells, is very good at finding the shortest distance between two points, provided they contain food. Researchers put a bit of oatmeal at two opposing vertices of a cuboctahedron with edge size one. The slime mold's job, and yours, is to find the minimal distance along the surface of the solid between these points. If there is more than one such path, multiply this distance by the number of these paths and report the result to 4 decimal places.

Paths which may be derived from each other by rotation or reflection are considered distinct.


Image credit: Wikimedia POV-Ray.
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