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001-es BibID:	BIBFORM103586
035-os BibID:	(Scopus)85096827133
Első szerző:	Vincze Csaba (matematikus)
Cím:	On equidistant polytopes in the Euclidean space / Csaba Vincze, Márk Oláh, Letícia Lengyel
Dátum:	2020
ISSN:	1944-4176 1944-4184
Megjegyzések:	An equidistant polytope is a special equidistant set in the space Rn all of whose boundary points have equal distances from two finite systems of points. Since one of the finite systems of the given points is required to be in the interior of the convex hull of the other one, we can speak about inner and outer focal points of the equidistant polytope. It is of type (q, p), where q is the number of the outer focal points and p is the number of the inner focal points. The equidistancy is the gen-eralization of convexity because a convex polytope can be given as an equidistant polytope of type (q, 1), where q >(=) n + 1. We present some general results about the basic properties of the equidistant polytopes: convex components, graph rep-resentations, connectedness, correspondence to the Voronoi decomposition of the space etc. In particular, we are interested in equidistant polytopes of dimension 2 (equidistant polygons). Equidistant polygons of type (3, 2) will be characterized in terms of a constructive (ruler-and-compass) process to recognize them. In general they are pentagons with exactly two concave angles such that the vertices at which the concave angles appear are joined by an inner diagonal related to the adjacent sides of the polygon in a special way via the three reflections theorem for concurrent lines. The last section is devoted to some special arrangements of the focal points to get the concave quadrangles as equidistant polygons of type (3, 2).
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk Convex geometry Equidistant sets Euclidean geometry
Megjelenés:	Involve, a Journal of Mathematics. - 13 : 4 (2020), p. 577-595. -
További szerzők:	Oláh Márk (1994-) (matematikus) Lengyel Letícia (1999-)
Pályázati támogatás:	EFOP-3.6.2-16-2017-00015 EFOP
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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