Geodesic
Geometry of Pentagonal Quasigroups
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 109

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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.
DOI : 10.2298/PIM141208013V
Classification : 20N05
Keywords: IM-quasigroup, parallelogram, midpoint, regular pentagon, regular decagon 
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     title = {Geometry of {Pentagonal} {Quasigroups}},
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Stipe Vidak. Geometry of Pentagonal Quasigroups. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 109 . doi: 10.2298/PIM141208013V

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