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Symmetries in hexagonal quasigroups

Vladimír VolenecMea Bombardelli — 2007

Archivum Mathematicum

Hexagonal quasigroup is idempotent, medial and semisymmetric quasigroup. In this article we define and study symmetries about a point, segment and ordered triple of points in hexagonal quasigroups. The main results are the theorems on composition of two and three symmetries.

Skewsquares in quadratical quasigroups

Vladimír VolenecRužica Kolar-Šuper — 2008

Commentationes Mathematicae Universitatis Carolinae

The concept of pseudosquare in a general quadratical quasigroup is introduced and connections to some other geometrical concepts are studied. The geometrical presentations of some proved statements are given in the quadratical quasigroup ( 1 + i 2 ) .

Affine regular decagons in GS-quasigroup

Vladimír VolenecZdenka Kolar-Begović — 2008

Commentationes Mathematicae Universitatis Carolinae

In this article 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 ( 1 2 ( 1 + 5 ) ) .

Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup

Vladimír VolenecZ. Kolar--BegovićR. Kolar--Šuper — 2012

Commentationes Mathematicae Universitatis Carolinae

The concept of the affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be introduced in this paper. The theorem of the unique determination of the affine regular icosahedron by means of its four vertices which satisfy certain conditions will be proved. The connection between affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be researched. The geometrical representation of the introduced concepts and relations between them...

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