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The appropriate notion of integer for surreal numbers.

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.

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.

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

Two (or more) intersecting curves that are perpendicular at their intersection are said to be orthogonal.