Prototile Octagon satisfying the Conway criterion. Sections AB and ED are shown in red, and the remaining segments are shown in color with a dot on the point of centrosymmetry.A tessellation of the above prototile meeting the Conway criterion.
In the mathematical theory of tessellations, the Conway criterion, named for the English mathematician John Horton Conway, is a sufficient rule for when a prototile will tile the plane. It consists of the following requirements:[1] The tile must be a closed topological disk with six consecutive points A, B, C, D, E, and F on the boundary such that:
the boundary part from A to B is congruent to the boundary part from E to D by a translation T where T(A) = E and T(B) = D.
each of the boundary parts BC, CD, EF, and FA is centrosymmetric—that is, each one is congruent to itself when rotated by 180-degrees around its midpoint.
some of the six points may coincide but at least three of them must be distinct.[2]
Any prototile satisfying Conway's criterion admits a periodic tiling of the plane—and does so using only 180-degree rotations.[1] The Conway criterion is a sufficient condition to prove that a prototile tiles the plane but not a necessary one. There are tiles that fail the criterion and still tile the plane.[3]
Every Conway tile is foldable into either an isotetrahedron or a rectangle dihedron and conversely, every net of an isotetrahedron or rectangle dihedron is a Conway tile.[4][3]
^ abWill It Tile? Try the Conway Criterion! by Doris Schattschneider Mathematics Magazine Vol. 53, No. 4 (Sep, 1980), pp. 224-233
^Periodic Tiling: Polygons in General
^ abTreks Into Intuitive Geometry: The World of Polygons and Polyhedra by Jin Akiyama and Kiyoko Matsunaga, Springer 2016, ISBN 9784431558415
^Cite error: The named reference video was invoked but never defined (see the help page).
mathematical theory of tessellations, the Conwaycriterion, named for the English mathematician John Horton Conway, is a sufficient rule for when a prototile...
polyhedron notation. In the theory of tessellations, he devised the Conwaycriterion which is a fast way to identify many prototiles that tile the plane...
uses 4-square shapes.) Each of the twelve pentominoes satisfies the Conwaycriterion; hence, every pentomino is capable of tiling the plane. Each chiral...
tessellation, the shape is said to tessellate or to tile the plane. The Conwaycriterion is a sufficient, but not necessary, set of rules for deciding whether...
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tessellation of the plane, any irregular hexagon which satisfies the Conwaycriterion will tile the plane. Pascal's theorem (also known as the "Hexagrammum...
Conwaycriterion – a criterion for identifying prototiles that admit a periodic tiling Conway group – any of the groups Co0, Co1, Co2, or Co3 Conway group...
satisfy the Conwaycriterion and 3 more can form a patch satisfying the criterion. Thus, only 4 heptominoes fail to satisfy the criterion and, in fact...
2 = 216 fixed hexominoes. Each of the 35 hexominoes satisfies the Conwaycriterion; hence, every hexomino is capable of tiling the plane. Although a complete...
the 1285 free nonominoes, 960 satisfy the Conwaycriterion and 88 more can form a patch satisfying the criterion. Two additional nonominoes admit tilings...
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the figure); it can tile the plane by 180-degree rotation using the Conwaycriterion. 16-sided golygon. Spirolateral 1690°1,3,6,8,11 32-sided golygon. Spirolateral...
Stefan; Winslow, Andrew (2016), "Polycube unfoldings satisfying Conway'scriterion" (PDF), 19th Japan Conference on Discrete and Computational Geometry...
wrapping, packing problems, wallpaper groups, pentagonal tilings, the Conwaycriterion for prototiles and Escher-like tilings of the plane by animal-shaped...
}})=\inf _{\delta }\ \sup _{\theta }\ R(\theta ,\delta )\ .} An alternative criterion in the decision theoretic framework is the Bayes estimator in the presence...
kotobank. Retrieved 27 December 2020. Marc Mohan "Crazed Fruit: The Criterion Collection" Deming, Mark. "Crazed Fruit (1956)". AllMovie. Retrieved 20...
submarine Tigershark, and Nobel Prize-winning scientist Sir Ian Hunt (Tom Conway). The United States Secretary of Defense (Jack Mulhall) leads the meeting;...
owner Dickinson is Charlie's father and hires three killers — Cole Wilson, Conway Twill, and Johnny "The Kid" Pickett — to bring Blake back "dead or alive"...
huge volumes of data and the existence of a semantic gap. The search criterion used by each search engine depends on its nature and purpose of the searches...
and The Films of Charlie Chaplin (1965) by Gerald D. McDonald, Michael Conway, and Mark Ricci. Screenshot of Charlie Chaplin (left) in scene with Henry...
1932 Herself Columbia Pictures Hollywood on Parade No. A-12 1933 Herself Criterion Productions/Paramount Hollywood on Parade No. B-1 1933 Herself The Candid...
The sequence of a n {\displaystyle a_{n}} satisfying the convergence criterion above is sometimes called a Blaschke sequence. A theorem of Gábor Szegő...
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