2003/04/30 by Hyeong-Chai Jeong, Jeong, Hyeong-Chai
Computer Science · Physics and Astronomy · #Cellular Automata and Applications #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0304690
7pages, 5figures
arxiv created 2003/04/30 · openalex publication_date 2003/04/30 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
The equivalence between quasi-unit-cell models and Penrose-tile models on the level of decorations is proved using inflation rules for Gummelt coverings with decorated decagons. Due to overlaps, Gummelt arrangement of decorated decagons gives rise to nine different (context-dependent) decagon decorations in the covering. The inflation rules for decagons for each of nine types are presented and shown that inflations from differently typed decagons always produce different decorations of inflated decagons. However, if the original decagon region is divided into ``equivalent'' rhombus Penrose tiles, typed-decagon arrangements in the tiles (of the same shape) become identical for the fourfold inflated decagons. This implies that a decagonal quasi-unit-cell model can be reinterpreted as a Penrose-tile model with fourfold deflated super-tiles.