Orthogonality-admitting inversive plane

From Groupprops
Jump to: navigation, search
This term is related to: incidence geometry
View other terms related to incidence geometry | View facts related to incidence geometry
This term is related to: inversive geometry
View other terms related to inversive geometry | View facts related to inversive geometry

Template:Inversive plane property

Definition

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

Facts

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