Regular Steiner polygons

Protecting regular polygons

The minimum number of mutually non-overlapping congruent copies of a convex body K so that they can touch K and prevent any other congruent copy of K from touching K without overlapping each other is called the protecting number of K. In this paper we prove that the 1 2 Arnfried Kemnitz, LL aszll o Szabb o, Zoltt an Ujvv ary-Menyhh art protecting number of any regular polygon is three or four, ...

Steiner Minimal Trees in Simple Polygons

An O(n log n) time and O(n) space algorithm for the Euclidean Steiner tree problem with four terminals in a simple polygon with n vertices is given. Its applicability to the problem of determining good quality solutions for any number of terminals is discussed.

Tiling with Regular Star Polygons

The Archimedean tilings (Figure 1) and polyhedra will be familiar to many readers. They have the property that the tiles of the tiling, or the faces of the polyhedron, are regular polygons, and that the vertices form a single orbit under the symmetries of the tiling or polyhedron. (Grünbaum and Shephard [1] use Archimedean, in relation to tilings, to refer to the sequence of polygons at each ve...

Regular polygons are most tolerant

Symmetric Colorings Of Regular Polygons

It is calculated the number of symmetric r-colorings of vertices of a regular n-gon and the number of equivalence classes of symmetric r-colorings [1, 2]. A coloring is symmetric if it is invariant in respect to some mirror symmetry with an axis crossing center of polygon and one of its vertices. Colorings are equivalent if we can get one from another by rotating about the polygon center.