A Hesse configuration is a set of nine non-collinear points in the projective plane over a field such that any line through two points of contains exactly three points of . Then there are 12 such lines through . A Hesse configuration exists if and only if the field contains a primitive third root of unity. For such the projective automorphism group acts transitively on all possible Hesse configurations.
The group of all symmetries that map onto itself has order 216 and it is isomorphic to the group of affine transformations of that have determinant 1. The stabilizer in of any of the 12 lines through is a cyclic subgroup of order three and is generated by these subgroups.
The symmetry group is isomorphic to where is a group of order 648 generated by reflections of order three and is its cyclic center of order three. The reflection group is called the Hesse group which appears as in the classification of finite complex reflection groups by Shephard and Todd.
|Date of creation||2013-03-22 14:04:04|
|Last modified on||2013-03-22 14:04:04|
|Last modified by||debosberg (3620)|