  An involution is usually defined as a mapping that is its own inverse. In
this paper, we study quaternion involutions that have the additional properties
of distribution over addition and multiplication. We review formal axioms for
such involutions, and we show that the quaternions have an infinite number of
involutions. We show that the conjugate of a quaternion may be expressed using
three mutually perpendicular involutions. We also show that any set of three
mutually perpendicular quaternion involutions is closed under composition.
Finally, we show that projection of a vector or quaternion can be expressed
concisely using involutions.
