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Affine regular decagons in GS-quasigroup. (English) Zbl 1192.20063

Summary: The “geometric” concept of the affine regular decagon in a general GS-quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS-quasigroup are explored. The geometrical presentation of all proved statements is given in the GS-quasigroup \(\mathbb{C}(\tfrac 12(1+\sqrt 5))\).

MSC:

20N05 Loops, quasigroups
51A15 Linear incidence geometric structures with parallelism
51A25 Algebraization in linear incidence geometry
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