THE TRIANGLE PATTERN — A NEW QUASIPERIODIC TILING WITH FIVEFOLD SYMMETRY

Abstract

We introduce a quasiperiodic tiling with fivefold symmetry that is built from two types of triangles, an acute and an obtuse one. An easy to computerize construction algorithm based on the dualization scheme is presented that creates the pattern not pointwise but tile by tile directly. We present the vertex statistics, the inflation rule, and the Fourier analysis for selected decorations with pointlike atoms. A connection to the planar Penrose pattern and to the 3D icosahedral quasilattice is briefly discussed.