Tilings and Patterns.

1988/01/01 by Solomon W. Golomb, Branko Grünbaum, G. C. Shephard · 31 citations
Mathematics · Materials Science · #Advanced Combinatorial Mathematics #Quasicrystal Structures and Properties #Graph theory and applications #Mathematics #Combinatorics

paper · doi:10.2307/2323457

openalex publication_date 1988/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/13

Abstract

Remarkable...It will surely remain the unique reference in this area for many years to come. Roger Penrose , Nature ...an outstanding achievement in mathematical education. Bulletin of The London Mathematical Society I am enormously impressed...Will be the definitive reference on tiling theory for many decades. Not only does the book bring together older results that have not been brought together before, but it contains a wealth of new material...I know of no comparable book. Martin Gardner

Cited by

• Convex pentagons that admit i-block transitive tilings
• Spanning trees on graphs and lattices inddimensions
• An aperiodic set of 13 Wang tiles
• The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy
• On column-convex and convex Carlitz polyominoes
• Golden Fields: A Case for the Heptagon
• Tiling Groupoids and Bratteli Diagrams
• Exact site percolation thresholds using a site-to-bond transformation and the star-triangle transformation
• Finite subdivision rules
• Reversibility and surjectivity problems of cellular automata
• Search methods for tile sets in patterned DNA self-assembly
• An infinite number of plane figures with Heesch number two
• Packing, covering and tiling in two-dimensional spaces
• A generalization of the Fibonacci word fractal and the Fibonacci snowflake
• The Crystallographic Restriction, Permutations, and Goldbach's Conjecture
• Uniform solution for uniform polyhedra
• Regular Packings on Periodic Lattices
• Some Properties of Lattice Substitution Systems
• Rich Polymorphic Behavior of Wigner Bilayers
• Energy landscape in a Penrose tiling
• Symmetry detection of auxetic behaviour in 2D frameworks
• On Bravais colourings of cyclotomic integers with class number one
• Transverse Laplacians for Substitution Tilings
• NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING
• An Efficient Exhaustive Search Algorithm for the Escherization Problem
• Isohedra with nonconvex faces
• Quasi-vertex-transitive maps on the plane
• A family of golden triangle tile patterns
• Voronoi diagrams—a survey of a fundamental geometric data structure
• One Tile to Rule Them All: Simulating Any Turing Machine, Tile Assembly\n System, or Tiling System with a Single Puzzle Piece
• An eight-fold optical quasicrystal with cold atoms
• 12 (number) [wikipedia]