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A Construction of a Skewaffine Structure in Laguerre Geometry

Andrzej Matraś (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

J. Andre constructed a skewaffine structure as a group space of a normally transitive group. In this paper his construction is used to describe the structure of the set of circles not passing through a point of a Laguerre plane. Sufficient conditions to ensure that this structure is a skewaffine plane are given.

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

Vladimír Volenec, Z. Kolar--Begović, R. 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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