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The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

The 16-cell beta_4 is the finite regular four-dimensional cross polytope with Schläfli symbol {3,3,4}. It is also known as the hyperoctahedron (Buekenhout and Parker 1998) or ...

The M_(22) graph, also known as the 77-graph, is a strongly regular graph on 77 nodes related to the Mathieu group M_(22) and to the Witt design. It is illustrated above in ...

For a graph vertex x of a graph, let Gamma_x and Delta_x denote the subgraphs of Gamma-x induced by the graph vertices adjacent to and nonadjacent to x, respectively. The ...

A dipyramid, also called a bipyramid, consists of two pyramids symmetrically placed base-to-base. The dipyramids are duals of the regular prisms. Their skeletons are the ...

A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

The augmented tridiminished icosahedron is Johnson solid J_(64), which is formed from augmentation of the triangular face adjecent to all three hexagons of the tridiminished ...

A piecewise regular function that 1. Has a finite number of finite discontinuities and 2. Has a finite number of extrema can be expanded in a Fourier series which converges ...

A statement which is rigorously not true. Regular two-valued logic allows statements to be only true or false, but fuzzy logic treats "truth" as a continuum which can have a ...