Orthogonality-admitting inversive plane

Definition
An inversive plane is said to be orthogonality-admitting if it admits an orthogonality.

For finite inversive planes

 * A finite inversive plane can admit at most one orthogonality
 * A finite inversive plane of even order admits exactly one orthogonality
 * A finite inversive plane of odd order admits an orthogonality if and only if it is Miquelian
 * A finite inversive plane is egglike if and only if it admits an orthogonality