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A mathematical object upon which an operator acts. For example, in the expression 1×2, the multiplication operator acts upon the operands 1 and 2.

An orbifold is the object obtained by identifying any two points of a map which are equivalent under some symmetry of the map's group.

A simple way to enumerate some types of groups due to J. H. Conway (Zwillinger 1995).

A geometry constructed without reference to measurement. The only primitive concepts are those of points and intermediacy. There are 10 axioms underlying ordered geometry.

Let (A,<=) and (B,<=) be disjoint totally ordered sets with order types alpha and beta. Then the ordinal sum is defined at set (C=A union B,<=) where, if c_1 and c_2 are both ...

Let (A,<=) and (B,<=) be totally ordered sets. Let C=A×B be the Cartesian product and define order as follows. For any a_1,a_2 in A and b_1,b_2 in B, 1. If a_1<a_2, then ...

A nonsingular linear map A:R^n->R^n is orientation-reversing if det(A)<0.

A bicupola in which the bases are in the same orientation.

A birotunda in which the bases are in the same orientation.

Coordinates defined by an orthocentric system.