Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup
Vladimír Volenec; Z. Kolar--Begović; R. Kolar--Šuper
Commentationes Mathematicae Universitatis Carolinae (2012)
- Volume: 53, Issue: 3, page 501-507
- ISSN: 0010-2628
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topVolenec, Vladimír, Kolar--Begović, Z., and Kolar--Šuper, R.. "Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup." Commentationes Mathematicae Universitatis Carolinae 53.3 (2012): 501-507. <http://eudml.org/doc/246647>.
@article{Volenec2012,
abstract = {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 $\mathbb \{C\}(\frac\{1\}\{2\}(1+\sqrt\{5\}))$.},
author = {Volenec, Vladimír, Kolar--Begović, Z., Kolar--Šuper, R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {GS-quasigroup; affine regular icosahedron; affine regular octahedron; affine spaces; GS-quasigroups; affine regular icosahedron; affine regular octahedron},
language = {eng},
number = {3},
pages = {501-507},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup},
url = {http://eudml.org/doc/246647},
volume = {53},
year = {2012},
}
TY - JOUR
AU - Volenec, Vladimír
AU - Kolar--Begović, Z.
AU - Kolar--Šuper, R.
TI - Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 3
SP - 501
EP - 507
AB - 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 $\mathbb {C}(\frac{1}{2}(1+\sqrt{5}))$.
LA - eng
KW - GS-quasigroup; affine regular icosahedron; affine regular octahedron; affine spaces; GS-quasigroups; affine regular icosahedron; affine regular octahedron
UR - http://eudml.org/doc/246647
ER -
References
top- Volenec V., GS-quasigroups, Časopis pěst. mat. 115 (1990), 307–318. Zbl1101.20042MR1071063
- Volenec V., Kolar Z., GS-trapezoids in GS-quasigroups, Math. Commun. 7 (2002), 143–158. Zbl1016.20052MR1952756
- Volenec V., Kolar-Begović Z., Affine regular pentagons in GS-quasigroups, Quasigroups Related Systems 12 (2004), 103–112. Zbl1073.20062MR2130583
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