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Triangular Boxes

Our main theorem will remind you of Billiard Path Destinations.

Destinations of Paths on Triangular Boxes:

If {$a,b\le c<a+b$}, then

• If {$c-a$} has more factors of 2 than {$c-b$}, then the path will end at the magenta corner.

• If {$c-b$} has more factors of 2 than {$c-a$}, then the path will end at cyan corner.

• If {$c-a$} and {$c-b$} have the same number of factors of 2, then the path will end at yellow corner.

Combining this result with {$\Delta$} and Destinations, we can describe an odd method of computing the destination for any box, whether it is triangular or not, using the Rubik's cube.

Back to Geometry.