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The tesseract is also called an 8-cell, C 8, (regular) octachoron, or cubic prism. It is the four-dimensional measure polytope, taken as a unit for hypervolume. [2] Coxeter labels it the γ 4 polytope. [3] The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope.
It is sometimes called a dekeract, a portmanteau of tesseract (the 4-cube) and deka-for ten (dimensions) in Greek, It can also be called an icosaronnon or icosa-10-tope as a 10 dimensional polytope, constructed from 20 regular facets. It is a part of an infinite family of polytopes, called hypercubes.
The most familiar 4-polytope is the tesseract or hypercube, the 4D analogue of the cube. The convex regular 4-polytopes can be ordered by size as a measure of 4-dimensional content (hypervolume) for the same radius. Each greater polytope in the sequence is rounder than its predecessor, enclosing more content [5] within the same radius. The 4 ...
The rhombic dodecahedron forms the maximal cross-section of a 24-cell, and also forms the hull of its vertex-first parallel projection into three dimensions. The rhombic dodecahedron can be decomposed into six congruent (but non-regular) square dipyramids meeting at a single vertex in the center; these form the images of six pairs of the 24 ...
The tesseract is one of 6 convex regular 4-polytopes. In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope.They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions.
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
It has 256 vertices, 1024 edges, 1792 square faces, 1792 cubic cells, 1120 tesseract 4-faces, 448 5-cube 5-faces, 112 6-cube 6-faces, and 16 7-cube 7-faces. It is represented by Schläfli symbol {4,3 6}, being composed of 3 7-cubes around each 6-face. It is called an octeract, a portmanteau of tesseract (the 4-cube) and oct for eight ...
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.