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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...

Alcune condizioni per la costruzione di un piano finito di traslazione

Alessandro Basile, Paolo Brutti (2001)

Bollettino dell'Unione Matematica Italiana

The construction of any finite translation plane depends on the appropriate determination of a partition P E of a Galois field E , together with a set A of automorphisms of E as a vector space. In this paper we obtain sufficient conditions on P E and A , so that a translation plane is produced. They are also necessary conditions when A = 1 . Particularly, we examine the case where E is a two-dimensional vector space. We prove that no translation planes are constructible by a single automorphism, other than...

Alcuni problemi di ricerca nelle geometrie di Galois

Francesco Mazzocca (2001)

Bollettino dell'Unione Matematica Italiana

We present a survey on classical problems of Galois geometries. More precisely we discuss some problems and results about ovals, hyperovals, caps, maximal arcs and blocking sets in projective planes and spaces over Galois fields.

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

Stoichev, Stoicho (2007)

Serdica Journal of Computing

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.Two heuristic algorithms (M65 and M52) for finding respectively unitals and maximal arcs in projective planes of order 16 are described. The exact algorithms based on exhaustive search are impractical because of the combinatorial explosion (huge number of combinations to be checked). Algorithms M65 and M52 use unions of orbits...

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