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A 3-dimensional handlebody is sometimes, particularly in older literature, referred to as a cube with handles. Examples. Let G be a connected finite graph embedded in Euclidean space of dimension n. Let V be a closed regular neighborhood of G in the Euclidean space. Then V is an n-dimensional handlebody. The graph G is called a spine of V.
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In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. 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 .
10-cube. In geometry, a 10-cube is a ten- dimensional hypercube. It has 1024 vertices, 5120 edges, 11520 square faces, 15360 cubic cells, 13440 tesseract 4-faces, 8064 5-cube 5-faces, 3360 6-cube 6-faces, 960 7-cube 7-faces, 180 8-cube 8-faces, and 20 9-cube 9-faces . It can be named by its Schläfli symbol {4,3 8 }, being composed of 3 9-cubes ...
Menger sponge. An illustration of M, the sponge after four iterations of the construction process. In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) [1] [2] [3] is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two ...
Rubik's family cubes of varying sizes. The original Rubik's cube was a mechanical 3×3×3 cube puzzle invented in 1974 by the Hungarian sculptor and professor of architecture Ernő Rubik. Extensions of the Rubik's cube have been around for a long time and come in both hardware and software forms. The major extension have been the availability ...
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