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  2. Four-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Four-dimensional_space

    Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.

  3. Tesseract - Wikipedia

    en.wikipedia.org/wiki/Tesseract

    In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. [1] 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.

  4. Hypercube - Wikipedia

    en.wikipedia.org/wiki/Hypercube

    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.

  5. 4-polytope - Wikipedia

    en.wikipedia.org/wiki/4-polytope

    The convex regular 4-polytopes are the four-dimensional analogues of the Platonic solids. 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.

  6. 5-cube - Wikipedia

    en.wikipedia.org/wiki/5-cube

    In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces. It is represented by Schläfli symbol {4,3,3,3} or {4,3 3 }, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge .

  7. Cantellated tesseract - Wikipedia

    en.wikipedia.org/wiki/Cantellated_tesseract

    This layout of cells in projection is analogous to the layout of faces in the projection of the truncated cube into 2 dimensions. Hence, the cantellated tesseract may be thought of as an analogue of the truncated cube in 4 dimensions. (It is not the only possible analogue; another close candidate is the truncated tesseract.)

  8. n-dimensional sequential move puzzle - Wikipedia

    en.wikipedia.org/wiki/N-dimensional_sequential...

    Another alternate-dimension puzzle is a view achievable in David Vanderschel's Magic Cube 3D. A 4-cube projected on to a 2D computer screen is an example of a general type of an n-dimensional puzzle projected on to a (n – 2)-dimensional space. The 3D analogue of this is to project the cube on to a 1-dimensional representation, which is what ...

  9. Clifford torus - Wikipedia

    en.wikipedia.org/wiki/Clifford_torus

    The relationship is similar to that of projecting the edges of a cube onto a sheet of paper. Such a projection creates a lower-dimensional image that accurately captures the connectivity of the cube edges, but also requires the arbitrary selection and removal of one of the three fully symmetric and interchangeable axes of the cube. If S 1 a and S 1