10 papers · 1 filter
On monohedral tilings of a regular polygon
Bushra Basit, Zsolt Lángi
A tiling of a topological disc by topological discs is called monohedral if all tiles are congruent. Maltby (J. Combin. Theory Ser. A 66: 40-52, 1994) characterized the monohedral…
An isoperimetric problem for three-dimensional parallelohedra
Zsolt Lángi
The aim of this note is to investigate isoperimetric-type problems for -dimensional parallelohedra; that is, for convex polyhedra whose translates tile the -dimensional Eucli…
On generalized Minkowski arrangements
Máté Kadlicskó, Zsolt Lángi
The concept of a Minkowski arrangement was introduced by Fejes Tóth in 1965 as a family of centrally symmetric convex bodies with the property that no member of the family contains…
Extremal convex polygons inscribed in a given convex polygon
Csenge Lili Ködmön, Zsolt Lángi
A convex polygon is inscribed in a convex polygon if every side of contains at least one vertex of . We present algorithms for finding a minimum area and a minimum p…
On the convex hull and homothetic convex hull functions of a convex body
Ákos G. Horváth, Zsolt Lángi
The aim of this note is to investigate the properties of the convex hull and the homothetic convex hull functions of a convex body in Euclidean -space, defined as the volume…
A solution to some problems of Conway and Guy on monostable polyhedra
Zsolt Lángi
A convex polyhedron is called monostable if it can rest in stable position only on one of its faces. The aim of this paper is to investigate three questions of Conway, regarding mo…