7 papers
Strongly self-dual polytopes
Ákos G. Horváth, István Prok
This article aims to study the class of strongly self-dual polytopes (ssd-polytopes for short), defined in a paper by Lovász \cite{lovasz}. He described a series of such polytopes…
An extremal problem of regular simplices-The higher dimensional case
Ákos G. Horváth
The new result of this paper connected with the following problem: Consider a supporting hyperplane of a regular simplex and its re ected image at this hyperplane. When will be the…
A note on the centers of a closed chain of circles
Ákos G. Horváth
In this note we prove that the centers of a closed chain of circles for which every two consecutive members meet in the points of two given circles form a tangent polygon of a coni…
Proper quadrics in the Euclidean -space
Ákos G. Horváth
In this paper we investigate the metric properties of quadrics and cones of the -dimensional Euclidean space. As applications of our formulas we give a more detailed description…
On the non-Paschian ordered planes
Ákos G. Horváth
We give a non-Paschian plane based on the property of betweenness which cannot be derived from an ordering of the points of a line. In this model there is no possibility to define…
Generalized Minkowski space with changing shape
Ákos G. Horváth
In earlier papers we changed the concept of the inner product to a more general one, to the so-called Minkowski product. This product changes on the tangent space hence we could in…