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The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus ...

The n-cycle complement graph C^__n is the graph complement of the cycle graph C_n. Cycle complement graphs are special cases of circulant graphs. The first few are ...

A (general) dodecahedron is a polyhedron having 12 faces. Examples include the Bilinski dodecahedron, decagonal prism, elongated square dipyramid (Johnson solid J_(15)), ...

A polyhedral graph having nine vertices. There are 2606 nonisomorphic nonahedral graphs, as first enumerated by Federico (1969; Duijvestijn and Federico 1981). Named ...

A parallelohedron is a space-filling polyhedron that fills space using an infinite number of similarly situated copies (Tutton 1964, pp. 567 and 723; Coxeter 1973, pp. ...

A polar zonohedron is a convex zonohedron derived from the star which joins opposite vertices of any right n-gonal prism (for n even) or antiprism (for n odd). The faces of ...

Clean tile is a game investigated by Buffon (1777) in which players bet on the number of different tiles a thrown coin will partially cover on a floor that is regularly ...

A square matrix with constant skew diagonals. In other words, a Hankel matrix is a matrix in which the (i,j)th entry depends only on the sum i+j. Such matrices are sometimes ...

An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...