Abstract
This chapter illustrates the n-widths of octahedra. It focuses on the Kolmogorov n-widths of the octahedron Bm1 = {x ε Rm:||x||1 ≦ 1} in lmp. Exact values of the Kolmogorov n-widths of octahedra are obtained by drawing on a connection with two-graphs. The chapter presents the establishment of a connection with regular 2-graphs to derive many exact values. It also presents a survey of some estimates, particularly those of Kašin, Maiorov, and Höllig. The chapter presents a condition where Xn is an optimal subspace if and only if the vectors Pek form a spherical eutactic star.
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