7/5/2023 0 Comments Rotational tessellation![]() ![]() We find a basis for `permissible vectors' yielding such symmetry for each size of copse. A copse is determined by a particular vector of node labels along one of its edges: the symmetry studied in the present paper corresponds to having identical vectors along all three edges of the copse. In the present paper we are particularly interested in copses and tessellations with rotational symmetry about each of a lattice of symmetry centres, either with or without reflexive symmetry as well. In Miller (1970) this was done for forests, slightly different from tessellations but with an identical theoretical approach. The purpose of the paper is to study which copses and tessellations exist, and to enumerate them, and to show how they may be constructed and listed. The tessellations are obtained by joining by an edge every pair of adjacent live nodes. We label the nodes individually with a 1 (called live nodes) or a 0 (called vacant nodes) in such a way that for the nodes on each triangle of one set with the same orientation the sum of the labels equals 0 (mod 2) the sum round unit triangles of the other orientation is not restricted. In any such background the unit triangles form two sets, of opposing orientations. It is concerned with `Copses' and `Tessellations' based on an infinite background of nodes at the vertices of a plane tessellation of unit equilateral triangles, forming either a finite larger equilateral triangle for a copse, or an infinite doubly periodic tessellation otherwise. This paper is a self-contained sequal to Miller (1970), entitled `Periodic forests of stunted trees'. ![]()
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