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Keywords:
GS-quasigroup; affine regular icosahedron; affine regular octahedron
GS-quasigroup; affine regular icosahedron; affine regular octahedron
Summary:
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 will be given in the GS-quasigroup $\mathbb{C}(\frac{1}{2}(1+\sqrt 5))$.
References:
[1] Volenec V.: GS-quasigroups. Časopis pěst. mat. 115 (1990), 307–318. MR 1071063 | Zbl 1101.20042
[2] Volenec V., Kolar Z.: GS-trapezoids in GS-quasigroups. Math. Commun. 7 (2002), 143–158. MR 1952756 | Zbl 1016.20052
[3] Volenec V., Kolar-Begović Z.: Affine regular pentagons in GS-quasigroups. Quasigroups Related Systems 12 (2004), 103–112. MR 2130583 | Zbl 1073.20062
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