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math.MG2016
Rectifications of Convex Polyhedra
Samuel Reid
A convex polyhedron, that is, a compact convex subset of which is the intersection of finitely many closed half-spaces, can be rectified by taking the convex hull of…
math.MG2016
On Arrangements of Six, Seven, and Eight Spheres: Maximal Bonding of Monatomic Ionic Compounds
Samuel Reid
Let be the solution to the contact number problem, i.e., the maximum number of touching pairs among any packing of congruent spheres in . We prove the long…
math.MG2016★ 3 cited
On Contact Numbers of Finite Lattice Sphere Packings and the Maximal Coordination of Monatomic Crystals
Samuel Reid
We algorithmically characterize the maximal contact number problem for finite congruent lattice sphere packings in and show that in this problem is eq…