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The set of points of X fixed by a group action are called the group's set of fixed points, defined by {x:gx=x for all g in G}. In some cases, there may not be a group action, ...

Let Gamma be a representation for a group of group order h, then sum_(R)Gamma_i(R)_(mn)Gamma_j(R)_(m^'n^')^*=h/(sqrt(l_il_j))delta_(ij)delta_(mm^')delta_(nn^'). The proof is ...

If G is a group, then the torsion elements Tor(G) of G (also called the torsion of G) are defined to be the set of elements g in G such that g^n=e for some natural number n, ...

The gyroelongated pentagonal bicupola is the Johnson solid J_(46), which consists of two pentagonal cupolas, one twisted with respect to the other, adjoined to a decagonal ...

One of the eight convex deltahedra built up from 16 equilateral triangles. It consists of two oppositely faced square pyramids rotated 45 degrees to each other and separated ...

The hacovercosine, also known as the hacoversed cosine and cohavercosine, is a little-used trigonometric function defined by hacovercos(z) = covercosz (1) = 1/2(1+sinz), (2) ...

A handlebody of type (n,k) is an n-dimensional manifold that is attained from the standard n-disk by attaching only k-D handles.

Hansen's problem is a problem in surveying described as follows. From the position of two known but inaccessible points A and B, determine the position of two unknown ...

A diagram expressing how the gluing operation that connects the handlebodies involved in a Heegaard splitting proceeds, usually by showing how the meridians of the handlebody ...

A Heegaard splitting of a connected orientable 3-manifold M is any way of expressing M as the union of two (3,1)-handlebodies along their boundaries. The boundary of such a ...