Multidimensional Convex Polyhedra and Searching for Magic Squares

Christopher J. Henrich

(retired)

Abstract

Magic squares of a given order can be found by a recursive search procedure. The search space, for squares of order 4, is a seven-dimensional polyhedron, embedded in 16-dimensional space. To search this polyhedron efficiently, one needs to know its bounding hyperspaces, and similar information for lower-dimensional projections of it.The Wolfram Library Archive package "Multidimensional Convex Polyhedra" was developed to solve this problem. Here, I show how to apply that package to this task.