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Geometry of pentagonal quasigroups

Pentagonal quasigroups are IM-quasigroups in which the additional identity of pentagonality holds. Motivated by the example C(q), where q is a solution of the equation q 4 − 3q 3 + 4q 2 − 2q + 1 = 0, some basic geometric concepts are introduced and studied in a general pentagonal quasigroup. Such concepts are parallelogram, midpoint of a segment, regular pentagon and regular decagon. Some theorems of Euclidean plane which use these concepts are stated and proved in pentagonal quasigroups.

IM-quasigroup, pentagonal quasigroup, regular pentagon, regular decagon

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