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  2. 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.

  3. Magic hypercube - Wikipedia

    en.wikipedia.org/wiki/Magic_hypercube

    The term nasik would apply to all dimensions of magic hypercubes in which the number of correctly summing paths (lines) through any cell of the hypercube is P = ⁠ 3 n − 1 / 2 ⁠. A pandiagonal magic square then would be a nasik square because 4 magic line pass through each of the m 2 cells. This was A.H. Frost’s original definition of nasik.

  4. Tesseract - Wikipedia

    en.wikipedia.org/wiki/Tesseract

    The regular complex polytope 4 {4} 2, , in has a real representation as a tesseract or 4-4 duoprism in 4-dimensional space. 4 {4} 2 has 16 vertices, and 8 4-edges. Its symmetry is 4 [4] 2, order 32. It also has a lower symmetry construction, , or 4 {}× 4 {}, with symmetry 4 [2] 4, order 16. This is the symmetry if the red and blue 4-edges are ...

  5. 10-cube - Wikipedia

    en.wikipedia.org/wiki/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.

  6. Magic cube classes - Wikipedia

    en.wikipedia.org/wiki/Magic_cube_classes

    The minimum requirements for a magic cube are: all rows, columns, pillars, and 4 space diagonals must sum to the same value. A simple magic cube contains no magic squares or not enough to qualify for the next class. The smallest normal simple magic cube is order 3. Minimum correct summations required = 3m 2 + 4 Diagonal:

  7. Hypercube graph - Wikipedia

    en.wikipedia.org/wiki/Hypercube_graph

    contains all the cycles of length 4, 6, ..., 2 n and is thus a bipancyclic graph. can be drawn as a unit distance graph in the Euclidean plane by using the construction of the hypercube graph from subsets of a set of n elements, choosing a distinct unit vector for each set element, and placing the vertex corresponding to the set S at the sum of ...

  8. 5-cube - Wikipedia

    en.wikipedia.org/wiki/5-cube

    It is a part of an infinite hypercube family. The dual of a 5-cube is the 5-orthoplex, of the infinite family of orthoplexes.. Applying an alternation operation, deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the demihypercubes.

  9. Keller's conjecture - Wikipedia

    en.wikipedia.org/wiki/Keller's_conjecture

    In this tiling of the plane by congruent squares, the green and violet squares meet edge-to-edge as do the blue and orange squares. In geometry, Keller's conjecture is the conjecture that in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire (n − 1)-dimensional face with each other.

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