In geometry, sphere packing in a cube is a three-dimensional sphere packing problem with the objective of packing spheres inside a cube. It is the three-dimensional...

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...

packing in a circle Sphere packing in a cube Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. (1991). Unsolved Problems in Geometry. New York:...

A sphere (from Greek σφαῖρα, sphaîra) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the...

In crystallography, atomic packing factor (APF), packing efficiency, or packing fraction is the fraction of volume in a crystal structure that is occupied...

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'...

{\displaystyle n} ⁠-cube with a point, or (inductively) by forming the suspension of an ⁠ ( n − 1 ) {\displaystyle (n-1)} ⁠-sphere. When ⁠ n ≥ 2 {\displaystyle...

optimal packing density of spheres could be surpassed by putting a sphere in each rhombicuboctahedron of the hypothetical packing which surpasses it.[citation...

inscribed circles must belong to a single sphere. For example, a rectangular cuboid has a midsphere only when it is a cube, because otherwise it has non-square...

Rubik's Cube Speedcubing Pocket Cube Rubik's Magic Rubik's Revenge Rush Hour (puzzle) Situation puzzle Sliding puzzle Snake cube Sokoban Soma cube Sphere packing...

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...

important "equator" getting the lowest density. Cube mapping records the environment as the six faces of a cube. The image distortion is markedly reduced,...

Dupin cyclide (inversion of a torus) Whitney umbrella Right conoid (a ruled surface) Apollonian gasket Apollonian sphere packing Blancmange curve Cantor dust...

plays a significant role in sphere packing problems and the classification of finite simple groups. In particular, the Leech lattice is obtained in a simple...

angles between pairs of circles in a circle packing whose corresponding polyhedron has the desired relation to its sphere. In any dimension higher than three...

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

packing spheres according to the cubic close(st) packing (CCP), also known as the face-centered cubic (fcc) packing, then sweeping away the spheres that...

Euclidean plane (a generalization of Thue's theorem, a 2-dimensional analog of the Kepler conjecture). He also investigated the sphere packing problem. He...

efficient way of packing together equal-sized spheres and stacking close-packed atomic planes in three dimensions. For example, if plane A lies beneath plane...

rwth-aachen.de. Sphere packings, lattices, and groups, by John Horton Conway, Neil James Alexander Sloane, Eiichi Bannai [1] Zwiebach, Barton (2004). A First Course...

dodecahedrille) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which has...

corresponds to a sphere packing of edge-length-diameter spheres centered on each vertex, or (dually) inscribed in each cell instead. In the hypercubic...

also be seen as a projection of an n-unit cube of spheres in 3-dimensional space, viewed on the diagonal axis. There are more spheres than circles because...

colours together" or "all numbers in order". The most famous of these puzzles is the original Rubik's Cube, a cubic puzzle in which each of the six faces can...

of a central atom in the structure. Each sphere in a cP lattice has coordination number 6, in a cI lattice 8, and in a cF lattice 12. Atomic packing factor...

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

the 3-spheres in the densest known packing of equal spheres in 4-space; its kissing number is 24, which is also the same as the kissing number in R4, as...

has a dual tessellation; the cell centers in a tessellation are cell vertices in its dual tessellation. The densest known regular sphere-packing in two...

In crystallography, interstitial sites, holes or voids are the empty space that exists between the packing of atoms (spheres) in the crystal structure...

(Chapters 16–17: Geometries on Three-manifolds I, II) George Maxwell, Sphere Packings and Hyperbolic Reflection Groups, JOURNAL OF ALGEBRA 79,78-97 (1982)...