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The gabled rhombohedra are a family of elongated gyrobifastigium that are space-filling. The equilateral elongated gyrobifastigium, illustrated above, is one such example.

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

The dual of the great ditrigonal dodecicosidodecahedron U_(42) and Wenninger dual W_(81).

A partially ordered set is defined as an ordered pair P=(X,<=). Here, X is called the ground set of P and <= is the partial order of P.

The hacoversine, also known as the hacoversed sine and cohaversine, is a little-used trigonometric function defined by hacoversin(z) = coversinz (1) = 1/2(1-sinz), (2) where ...

A pyramid with a heptagonal base. The heptagonal pyramid is one of the 257 convex octahedra.

A figurate number which is equal to the cubic number n^3. The first few are 1, 8, 27, 64, ... (OEIS A000578).

A hexomino is a 6-polyomino. There are 35 free hexominoes (illustrated above), 60 one-sided hexominoes, and 216 fixed hexominoes.

A knot that secures a rope to a post, ring, another rope, etc., but does not keep its shape by itself.

The inversion of a horn torus. If the inversion center lies on the torus, then the horn cyclide degenerates to a parabolic horn cyclide.