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A polygonal number of the form O_n=n(3n-2). The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is ...

A deltahedron is a polyhedron whose faces are congruent equilateral triangles (Wells 1986, p. 73). Note that polyhedra whose faces could be triangulated so as to be composed ...

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 ...

If r experiments are performed with n_i possible outcomes for each experiment i=1,2,...,r, then there are a total of product_(i=1)^(r)n_i possible outcomes.

A fractal process for which H>1/2, so r>0.

A smooth manifold with a Poisson bracket defined on its function space.

The number of cells in a generalized Chinese checkers board (or "centered" hexagram). Unlike the polygonal numbers, there is ambiguity in the case of the star numbers as to ...

Possessing a three equivalent modes.

An Aztec diamond of order n is the region obtained from four staircase shapes of height n by gluing them together along the straight edges. It can therefore be defined as the ...

The above two figures are rearrangements of each other, with the corresponding triangles and polyominoes having the same areas. Nevertheless, the bottom figure has an area ...