# Shortest Distance On Tesseract

**Geometry**Level 5

Find this shortest distance in \(\text{ mm}\).

Note: We could say the vertices of the tesseract are at \((0,0,0,0), (0,0,0,42), (0,0,42,0), ....,(42,42,42,42)\), so that Brilli the Ant would be at \((21,17,0,0)\), and the micro-wormhole he needs to get to would be at \((21,21,42,42)\). He can travel only on the surfaces of the tesseract, i.e. at all points of its path, \(2\) of the point coordinates must either be \(0\) or \(42\).

The surfaces of the tesseract appear kind of like flat soap bubbles in this animation, bounded by straight edges.

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