finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed. The question of packing finitely...

In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical...

Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It...

which is homeomorphic to the sphere. The circle packing theorem guarantees the existence of a circle packing with finitely many circles whose intersection...

structures offer the best lattice packing of spheres, and is believed to be the optimal of all packings. With 'simple' sphere packings in three dimensions ('simple'...

block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into...

defines the translative packing constant of that body. Atomic packing factor Sphere packing List of shapes with known packing constant Groemer, H. (1986)...

unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement of spheres) in...

this area include: Circle packings Sphere packings Kepler conjecture Quasicrystals Aperiodic tilings Periodic graph Finite subdivision rules Structural...

conjecture could be carried over to the Euclidean case. Finite Field Kakeya Conjecture: Let F be a finite field, let K ⊆ Fn be a Kakeya set, i.e. for each vector...

configuration for the packing of four equal spheres. The dense random packing of hard spheres problem can thus be mapped on the tetrahedral packing problem. It...

lowest maximum packing density of all centrally-symmetric convex plane sets Sphere packing problems, including the density of the densest packing in dimensions...

mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater...

Apollonian network, a graph derived from finite subsets of the Apollonian gasket Apollonian sphere packing, a three-dimensional generalization of the...

randomly pack in a finite container up to a packing fraction between 75% and 76%. In 2008, Chen was the first to propose a packing of hard, regular tetrahedra...

A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line...

contributions to group theory, the representation theory of finite groups, the geometry of numbers, sphere packing, and quadratic forms. He is the namesake of Blichfeldt's...

investigated the sphere packing problem. He was the first to show, in 1953, that proof of the Kepler conjecture can be reduced to a finite case analysis...

ISBN 052120125X. Boerdijk, A.H. (1952). "Some remarks concerning close-packing of equal spheres". Philips Res. Rep. 7: 303–313. Fuller, R.Buckminster (1975). Applewhite...

Hyperplane Lattice Ehrhart polynomial Leech lattice Minkowski's theorem Packing Sphere packing Kepler conjecture Kissing number problem Honeycomb Andreini tessellation...

n-dimensional spheres of a fixed radius in Rn so that no two spheres overlap. Lattice packings are special types of sphere packings where the spheres are centered...

touching quadruples (3-simplices) in a sphere packing. The simplicial complex recognition problem is: given a finite simplicial complex, decide whether it...

\right)\right)+o\left(1\right)} Block codes are tied to the sphere packing problem which has received some attention over the years. In two dimensions...

questions about lattices and sphere packing in Euclidean space. The first part of the problem asks whether there are only finitely many essentially different...

atomic packing factor (APF). This is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts...

In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges...

on the density of sphere packings using the Poisson summation formula, which subsequently led to a proof of optimal sphere packings in dimension 8 and...

polyhedra Conway polynomial (finite fields) – an irreducible polynomial used in finite field theory Conway puzzle – a packing problem invented by Conway...

extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs...

For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere (the insphere) tangent to the tetrahedron's...