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2. Packing problems - Wikipedia

   en.wikipedia.org/wiki/Packing_problems

   Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and ...

3. Hoffman's packing puzzle - Wikipedia

   en.wikipedia.org/wiki/Hoffman's_packing_puzzle

   Hoffman's packing puzzle, disassembled. Hoffman's packing puzzle is an assembly puzzle named after Dean G. Hoffman, who described it in 1978. [1] The puzzle consists of 27 identical rectangular cuboids, each of whose edges have three different lengths. Its goal is to assemble them all to fit within a cube whose edge length is the sum of the ...

4. Rectified 9-cubes - Wikipedia

   en.wikipedia.org/wiki/Rectified_9-cubes

   Rectified 9-cubes. In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube . There are 9 rectifications of the 9-cube. The zeroth is the 9-cube itself, and the 8th is the dual 9-orthoplex. Vertices of the rectified 9-cube are located at the edge-centers of the 9-orthoplex.

5. 9-cube - Wikipedia

   en.wikipedia.org/wiki/9-cube

   9-cube. In geometry, a 9-cube is a nine- dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces . It can be named by its Schläfli symbol {4,3 7 }, being composed of three 8-cubes around each 7-face.

6. Rectified 9-orthoplexes - Wikipedia

   en.wikipedia.org/wiki/Rectified_9-orthoplexes

   The rectified 9-orthoplex is the vertex figure for the demienneractic honeycomb.. or Alternate names. rectified enneacross (Acronym riv) (Jonathan Bowers) Construction. There are two Coxeter groups associated with the rectified 9-orthoplex, one with the C 9 or [4,3 7] Coxeter group, and a lower symmetry with two copies of 8-orthoplex facets, alternating, with the D 9 or [3 6,1,1] Coxeter group.

7. Sphere packing in a cube - Wikipedia

   en.wikipedia.org/wiki/Sphere_packing_in_a_cube

   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 equivalent of the circle packing in a square problem in two dimensions. The problem consists of determining the optimal packing of a given number of spheres inside the cube.