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The symmetry operation (x,y,z)->(x,y,-z), etc., which is equivalent to 2^_, where the bar denotes an improper rotation.

A surface given by the form z=F(x,y).

An algebraic surface of degree 9. Enneper's minimal surface is an example of a nonic surface.

An angle which is not a right angle or a multiple of a right angle.

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

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

Orthogonal contravariant and covariant satisfy g_(ik)g^(ij)=delta_k^j, where delta_j^k is the Kronecker delta.

The map x^' = x+1 (1) y^' = 2x+y+1, (2) which leaves the parabola x^('2)-y^'=(x+1)^2-(2x+y+1)=x^2-y (3) invariant.

A tensor g whose discriminant satisfies g=g_(11)g_(22)-g_(12)^2>0.

The product of any number of perspectivities.