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When the elongated square pyramid with unit edge lengths (i.e., an equilateral obelisk) is truncated by a plane passing through opposite corners of its square base and the ...

A nonzero module M over a ring R whose only submodules are the module itself and the zero module. It is also called a simple module, and in fact this is the name more ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

An oriented link is a link for which each connected component has been given an orientation. As oriented links are equivalent, if there is an orientation preserving ...

A curve alpha on a regular surface M is a principal curve iff the velocity alpha^' always points in a principal direction, i.e., S(alpha^')=kappa_ialpha^', where S is the ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

The sawtooth wave, called the "castle rim function" by Trott (2004, p. 228), is the periodic function given by S(x)=Afrac(x/T+phi), (1) where frac(x) is the fractional part ...

R. Whorf found that there are probably several thousand stellations of the small triakis octahedron (Wenninger 1983, p. 36). In particular, the convex hulls of the great ...

A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...