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Original scientific paper
https://doi.org/10.31896/k.21.8

An Affine Regular Icosahedron Inscribed in an Affine Regular Octahedron in a GS-Quasigroup

Zdenka Kolar-Begović   ORCID icon orcid.org/0000-0001-8710-8628 ; Department of Mathematics, University of Osijek, Osijek, Croatia

Fulltext: english, pdf (227 KB) pages 3-5 downloads: 93* cite
APA 6th Edition
Kolar-Begović, Z. (2017). An Affine Regular Icosahedron Inscribed in an Affine Regular Octahedron in a GS-Quasigroup. KoG, 21 (21), 3-5. https://doi.org/10.31896/k.21.8
MLA 8th Edition
Kolar-Begović, Zdenka. "An Affine Regular Icosahedron Inscribed in an Affine Regular Octahedron in a GS-Quasigroup." KoG, vol. 21, no. 21, 2017, pp. 3-5. https://doi.org/10.31896/k.21.8. Accessed 19 Oct. 2019.
Chicago 17th Edition
Kolar-Begović, Zdenka. "An Affine Regular Icosahedron Inscribed in an Affine Regular Octahedron in a GS-Quasigroup." KoG 21, no. 21 (2017): 3-5. https://doi.org/10.31896/k.21.8
Harvard
Kolar-Begović, Z. (2017). 'An Affine Regular Icosahedron Inscribed in an Affine Regular Octahedron in a GS-Quasigroup', KoG, 21(21), pp. 3-5. https://doi.org/10.31896/k.21.8
Vancouver
Kolar-Begović Z. An Affine Regular Icosahedron Inscribed in an Affine Regular Octahedron in a GS-Quasigroup. KoG [Internet]. 2017 [cited 2019 October 19];21(21):3-5. https://doi.org/10.31896/k.21.8
IEEE
Z. Kolar-Begović, "An Affine Regular Icosahedron Inscribed in an Affine Regular Octahedron in a GS-Quasigroup", KoG, vol.21, no. 21, pp. 3-5, 2017. [Online]. https://doi.org/10.31896/k.21.8

Abstracts
A golden section quasigroup or shortly a GS-quasigroup is an idempotent quasigroup which satis es the identities a\dot (ab \dot c) \dot c = b; a\dot (a \dot bc) \dot c = b. The concept of a GS-quasigroup was introduced by VOLENEC. A number of geometric concepts can be introduced in a general GS-quasigroup by means of the binary quasigroup operation. In this paper, it is proved that for any affine regular octahedron there is an affine regular icosahedron which is inscribed in the given affine regular octahedron. This is proved by means of the identities and relations which are valid in a general GS-quasigrup. The geometrical presentation in the GS-quasigroup C(\frac{1}{2} (1 +\sqrt{5})) suggests how a geometrical consequence may be derived from the statements proven in a purely algebraic manner.

Keywords
GS-quasigroup; GS-trapezoid; affine regular icosahedron; affine regular octahedron

Hrčak ID: 192184

URI
https://hrcak.srce.hr/192184

[croatian]

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