In the field of combinatorial geometry one studies properties of countable geometric objects.

Configurations

A configuration is a finite number of points and lines, such that to each points is the same number of lines allocated, and to each point the same number of lines.

Regular bodies und crystals

A regular body/polyhedron is a subset of the three dimensional space, which is limited by planes. The surface contains of straight plane fragments, lines and vertices. Crystals can be regarded as regular integer point systems. They are classified by their symmetries.

Isometry groups

Isometry groups describe movement in the plane or the three dimensional space. Therefore mappings which map geometric objects to congruent ones.

Polyhedrons

A regular body/polyhedron is a subset of the three dimensional space, which is limited by planes. The surface contains of straight plane fragments, lines and vertices.

4-dimensional regular configurations

To visulize a four dimensional object one has to project.