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2. 8-cube - Wikipedia

   en.wikipedia.org/wiki/8-cube

   This 8-cube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertex-edge-vertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:8:28:56:70:56:28:8:1.

3. 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 ...

4. Truncated 8-cubes - Wikipedia

   en.wikipedia.org/wiki/Truncated_8-cubes

   Truncated 8-cubes. In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube. There are unique 7 degrees of truncation for the 8-cube. Vertices of the truncation 8-cube are located as pairs on the edge of the 8-cube. Vertices of the bitruncated 8-cube are located on the square ...

5. Tesseract - Wikipedia

   en.wikipedia.org/wiki/Tesseract

   Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C 8, (regular) octachoron, or cubic ...

6. Sphere packing - Wikipedia

   en.wikipedia.org/wiki/Sphere_packing

   Sphere packing finds practical application in the stacking of cannonballs. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three- dimensional Euclidean space. However, sphere packing problems can be ...

7. Rectified 8-cubes - Wikipedia

   en.wikipedia.org/wiki/Rectified_8-cubes

   Rectified 8-cubes. In eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube . There are unique 8 degrees of rectifications, the zeroth being the 8-cube, and the 7th and last being the 8-orthoplex. Vertices of the rectified 8-cube are located at the edge-centers of the 8-cube.