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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

38 votes
7 answers
5k views

Shortest path connecting two opposite points on a cube

Is it true, that a path connecting two opposite points (i.e. such that the segment joining them passes through the centre of mass of the cube) on the surface of the $d$-dimensional unit cube (with $d> …
Arseniy Akopyan's user avatar