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There are a number of attractive polyhedron compounds consisting of six octahedra. The two illustrated above can be constructed as the duals of cube 6-compounds. These ...

The specification of a curve, surface, etc., by means of one or more variables which are allowed to take on values in a given specified range.

The pentagonal gyrocupolarotunda is a convex equilateral solid that is Johnson solid J_(33). The unit pentagonal gyrocupolarotunda has volume V=5/(12)(11+5sqrt(5)) (1) and ...

The dimension of a partially ordered set P=(X,<=) is the size of the smallest realizer of P. Equivalently, it is the smallest integer d such that P is isomorphic to a ...

Quasirandom numbers are numbers selected from a quasirandom sequence. Such numbers are useful in computational problems such as quasi-Monte Carlo integration.

One of the straight lines sweeping out a ruled surface. The rulings on a ruled surface are asymptotic curves.

A polygon whose vertices do not all lie in a plane.

Johnson solid J_(61).

The tridiminished icosahedron is Johnson solid J_(63). Interestingly, its skeleton has the same degree sequence as the triangular cupola.

The exact values of cos(pi/18) and sin(pi/18) can be given by infinite nested radicals sin(pi/(18))=1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2-...)))), where the sequence of signs +, +, ...