1. A mathematical transformation or mapping in which a point is mapped to another point such that applying the transformation twice returns the original point, with the additional property that the transformation exhibits excessive or extreme self-referential behavior.
Usage: technical; mathematics; rare in general usage
2. In geometry, a type of involution (a self-inverse transformation) characterized by particularly complex or intensified properties.
Usage: technical; geometry; specialized

Examples

• The hyperinvolution in this projective space exhibits unusual symmetry properties.
• Mathematicians studied the hyperinvolution to understand its fixed points.
• The transformation defined a hyperinvolution on the algebraic variety.