This form of the aperiodic Penrose tiling has two prototiles, a thick rhombus (shown blue in the figure) and a thin rhombus (green).
In mathematics, a prototile is one of the shapes of a tile in a tessellation.[1]
^Cederberg, Judith N. (2001), A Course in Modern Geometries, Undergraduate Texts in Mathematics (2nd ed.), Springer-Verlag, p. 174, ISBN 978-0-387-98972-3.
In mathematics, a prototile is one of the shapes of a tile in a tessellation. A tessellation of the plane or of any other space is a cover of the space...
tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles). A tessellation of space, also known as a space filling or honeycomb...
problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space...
only a finite number of shapes. These shapes are called prototiles, and a set of prototiles is said to admit a tiling or tile the plane if there is a...
5, 6, 7, 8, 9, and 13 allow parametric possibilities with nonconvex prototiles. Periodic tilings are characterised by their wallpaper group symmetry...
the Voronoi diagram forms a honeycomb in which there is only a single prototile shape, the shape of these Voronoi cells. This shape is called a plesiohedron...
A set of prototiles is aperiodic if copies of the prototiles can be assembled to create tilings, such that all possible tessellation patterns are non-periodic...
Rhoads, Glenn C. (2003). Planar Tilings and the Search for an Aperiodic Prototile. PhD dissertation, Rutgers University. Gardner, Martin (August 1975)....
English mathematician John Horton Conway, is a sufficient rule for when a prototile will tile the plane. It consists of the following requirements: The tile...
arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings...
regular octagon. The Ammann–Beenker tiling is a nonperiodic tesselation of prototiles that feature prominent octagonal silver eightfold symmetry, that is the...
In geometry, an Ammann A1 tiling is a tiling from the 6 piece prototile set shown on the right. They were found in 1977 by Robert Ammann. Ammann was inspired...
einstein problem – does there exist a two-dimensional shape that forms the prototile for an aperiodic tiling, but not for any periodic tiling? Falconer's conjecture:...
together. Several variations of this tiling have been studied, all of whose prototiles exhibit the golden ratio: Penrose's original version of this tiling used...
Rhoads, Glenn C. (2003). Planar Tilings and the Search for an Aperiodic Prototile. PhD dissertation, Rutgers University. Mathematische Basteleien: Hexominos...
he devised the Conway criterion which is a fast way to identify many prototiles that tile the plane. He investigated lattices in higher dimensions and...
Rhoads, Glenn C. (2003). Planar Tilings and the Search for an Aperiodic Prototile. PhD dissertation, Rutgers University. Grünbaum and Shephard, section...
dodecahedron tessellations in 3 dimensions. It is also possible to subdivide the prototiles of certain hexagonal tilings by two, three, four or nine equal pentagons:...
tile substitutions generate aperiodic tilings, which are tilings whose prototiles do not admit any tiling with translational symmetry. The most famous of...
from its Italian name Partito Democratico Cristiano Sammarinese) SCD prototile, a space-filling polyhedron South Carolina Department of Public Safety...
tessellations, tessellations generated by reflections across each edge of a prototile. It is one of 7 dual uniform tilings in hexagonal symmetry, including...
Image Description Dimension Packing constant Comments Monohedral prototiles all 1 Shapes such that congruent copies can form a tiling of space Circle,...
tessellates the plane with congruent copies of itself. In this case, the prototile is an elongated irregular nonagon, or nine-sided figure. The most interesting...
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