Inversion

An inversion is an improper isometry of Euclidean space.

When used as an operator in the sandwich antiproduct, a unitized point $$\mathbf F = F_{px}\mathbf e_1 + F_{py}\mathbf e_2 + F_{pz}\mathbf e_3 + \mathbf e_4$$ is a specific kind of flector that performs an inversion through $$\mathbf F$$.

Calculation
The exact inversion calculations for points, lines, and planes are shown in the following table.