2008/08/08 by Manuela Heuer, Heuer, Manuela
Computer Science · Mathematics · #05A15 #11R52 #52C07 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:05A15 #msc:11R52 #msc:52C07
paper · pdf · doi:10.48550/arxiv.0808.1228
8 pages, paper presented at ICQ10 (Zurich, Switzerland)
arxiv created 2008/08/08 · openalex publication_date 2008/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A natural way to describe the Penrose tiling employs the projection method on the basis of the root lattice A4 or its dual. Properties of these lattices are thus related to properties of the Penrose tiling. Moreover, the root lattice A4 appears in various other contexts such as sphere packings, efficient coding schemes and lattice quantizers. Here, the lattice A4 is considered within the icosian ring, whose rich arithmetic structure leads to parametrisations of the similar sublattices and the coincidence rotations of A4 and its dual lattice. These parametrisations, both in terms of a single icosian, imply an index formula for the corresponding sublattices. The results are encapsulated in Dirichlet series generating functions. For every index, they provide the number of distinct similar sublattices as well as the number of coincidence rotations of A4 and its dual.