Euclidean geometry

treatise by Archimedes

lattice group in Euclidean space whose points are integer n-tuples

𝑛‐dimensional polytope each of whose vertices are adjacent to exactly 𝑛 edges

intersection of a line and a plane can be the empty set, a point, or a line

certain parallelograms occurring in a gnomon have areas of equal size

In geometry, a gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose axis passes through the center of rotational symmetry. In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a mirror, called a gyration point.

polytope whose facets are all simplices