Point groups in three dimensions the finite subgroups of SO(3), are: the cyclic groups "C" (the rotation group of a canonical pyramid), the dihedral groups "D" (the rotation group of a uniform prism, or canonical bipyramid), and the rotation groups "T", "O" and "I" of a regular tetrahedron, octahedron/cube and icosahedron/dodecahedron. In particular, the dihedral groups "D", "D" etc. are the rotation groups of plane regular polygons embedded in three-dimensional space, and such a figure may be considered as a degenerate regular prism. Therefore, it is also called a "dihedron" (Greek: solid with two faces), which explains the name "dihedral group". The rotation group of
Benz plane oriented lines and circles. Both geometries are isomorphic.) As for the Möbius plane, there exists a 3-dimensional model: the geometry of the elliptic plane sections on an orthogonal cylinder (in formula_7). An abstraction leads (analogously to the Möbius plane) to the axiomatic Laguerre plane. Starting from formula_8 and merging the lines formula_9 with the hyperbolas formula_10 in order to get the set of blocks, the following idea homogenizes the incidence structure: Add to any line the point formula_11 and to any hyperbola formula_10 the two points formula_13. Hence the point set is formula_14. This geometry of the hyperbolas is called