# Biggest Little Polyhedron

Biggest Little Polyhedron

A polyhedron has vertices. The greatest distance between vertices is 1. What is the maximum volume of the polyhedron? This is known as the biggest little polyhedron problem.

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For four vertices, the solution is trivially the regular tetrahedron.

Five vertices require an equilateral triangle and a perpendicular unit line; this was solved in 1976 [1].

Six vertices require a more complex solution, which was solved to four digits of accuracy in 2003 [2, 3].

The author found exact solutions for 6, 7, 8, 9, 10, 11, and 16 points [4, 5]. This Demonstration contains those solutions, as well as the best known solutions up to 128 points. Oleg Vlasii improved many of these values.