Results 31 to 40 of about 6,990 (214)
Journal of Combinatorial Theory, Series A, 2011 We show that a single prototile can fill space uniformly but not admit a periodic tiling. A two-dimensional, hexagonal prototile with markings that enforce local matching rules is proven to be aperiodic by two independent methods. The space--filling tiling that can be built from copies of the prototile has the structure of a union of honeycombs with ...
Socolar, Joshua E.S., Taylor, Joan M.
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Chiral surfaces self-assembling in one-component systems with isotropic interactions [PDF]
, 2012 We show that chiral symmetry can be broken spontaneously in one-component systems with isotropic interactions, i.e. many-particle systems having maximal a priori symmetry.
E. Edlund +6 more
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Imaginary Cubes and Their Puzzles
Algorithms, 2012 Imaginary cubes are three dimensional objects which have square silhouette projections in three orthogonal ways just as a cube has. In this paper, we study imaginary cubes and present assembly puzzles based on them.
Hideki Tsuiki
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On the Penrose and Taylor–Socolar hexagonal tilings [PDF]
Acta Crystallographica Section A Foundations and Advances, 2017 The intimate relationship between the Penrose and the Taylor–Socolar tilings is studied, within both the context of double hexagon tiles and the algebraic context of hierarchical inverse sequences of triangular lattices. This unified approach produces both types of tilings together, clarifies their relationship and offers straightforward proofs of ...
Lee, Jeong-Yup, Moody, Robert V.
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Dodecagonal quasicrystal in Mn-based quaternary alloys containing Cr, Ni and Si [PDF]
, 2015 A dodecagonal quasicrystal showing 12-fold symmetry forms in Mn-rich quaternary alloys containing 5.5 or 7.5 at.% Cr, 5.0 at.% Ni and 17.5 at.% Si.
Ishimasa, Tsutomu, Iwami, Shuhei
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Alexandria Engineering Journal, 2019 In the 21st century, many contemporary architectural trends and tools such as the parametric design are having an influence the design of building envelope.
Ahmed Rashwan +2 more
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The Crossing Number of The Hexagonal Graph H3,n
Discussiones Mathematicae Graph Theory, 2019 In [C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus S1 and the ...
Wang Jing +2 more
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Mirrors with Regular Hexagonal Segments [PDF]
, 2003 The point-spread function and emissivity are calculated for a mirror made from regular hexagonal segments of just a few different sizes. A mirror of this type has many similar segments, which is an advantage for manufacturing, and for an ~f/1 mirror with
Amodei, Dario, Padin, Stephen
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Elliptically Distributed Lozenge Tilings of a Hexagon [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 We present a detailed study of a four parameter family of elliptic weights on tilings of a hexagon introduced by Borodin, Gorin and Rains, generalizing some of their results. In the process, we connect the combinatorics of the model with the theory of elliptic special functions.
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Spectral minimal partitions for a family of tori
, 2016 We study partitions of the rectangular two-dimensional flat torus of length 1 and width b into k domains, with b a parameter in (0, 1] and k an integer.
Bonnaillie-Noël, Virginie +1 more
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