Translation Plane
for Rosh Hashanah
Figure A
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From the website of Priv.-Doz. Dr. H. Klein, The Translation Plane of Order Nine There are exactly four projective planes of order nine, and one of these planes is a non-Desarguesian translation plane. Theorem. Up to isomorphism, there exists exactly one non-Desarguesian translation plane of order 9. This translation plane is defined by a spreadset in a 2-dimensional vector space over the field GF(3), consisting of the following matrices.
  As it turns out, the coordinatizing quasifield is a nearfield. Moreover the non-Desarguesian translation plane of order 9 has Lenz-Barlotti type IVa.3. |
Two versions of the defining spreadset for this plane are shown in Figure A. In the left part of Fig. A, the matrices of Dr. Klein are altered by the use of “2” instead of