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An E_8 polytope is a polytope having the symmetry of the exceptional simple Lie groups E_8 of dimension 248. There are 255 uniform polytopes with E_8 symmetry in 8 ...

A Lie algebra over an algebraically closed field is called exceptional if it is constructed from one of the root systems E_6, E_7, E_8, F_4, and G_2 by the Chevalley ...

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 ...

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 ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

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 ...

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 ...

The n-wheel complement graph W^__n is the graph complement of the n-wheel graph. For n>4, W^__n is isomorphic to the graph disjoint union of a circulant graph ...