The Symmetries of Things

Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim

doi:10.1201/b21368

Cited by 135 publications

(187 citation statements)

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“…In geometry, the feasibility of specific tessellations (tilings) depends on the curvature of the underlying surface . The chemically relevant hexagonal tiling (Figure B), which provides a model of benzenoid ring fusion, fits on surfaces with constant zero Gaussian curvature ( κ =0), and notably on the Euclidean plane (as in graphene and nanographenes) and on the cylinder (as in carbon nanotubes).…”

Section: Figurementioning

confidence: 99%

Octulene: A Hyperbolic Molecular Belt that Binds Chloride Anions

et al. 2016

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Octulene,t he higher homologue of kekulene and septulene,was synthesized using the fold-in method. This new hydrocarbon macrocycle contains al arge 24-membered inner circuit, which is peripherally fused to 24 benzenerings.Such an arrangement produces considerable hyperbolic distortion of the p-conjugated surface.T he consequences of distortion in octulene were explored using photophysical methods,w hich revealed ar educed electronic band gap and greater flexibility of the p system. Octulene contains af unctional cavity with ad iameter larger than 5.5 that is capable of efficiently binding the chloride anion in an onpolar solvent (K a = 2.2(4) 10 4 m À1 ,1 %d ichloromethane (DCM) in benzene). The octulene-chloride interaction is stabilized by eight weak C(sp 2 )H···Cl bonds,p roviding the first example of ah ydrocarbon-based anion receptor.

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Section: Figurementioning

confidence: 99%

Octulene: A Hyperbolic Molecular Belt that Binds Chloride Anions

et al. 2016

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“…An idea would be to design a dilational sphere by means of spherical symmetries. There have been studies researching spherical symmetries [37] that could act useful in finding innovative designs based on different types of symmetries from the standard Bravais lattices. The sphere is chosen as a starting point for its simplistic threedimensional form.…”

Section: Discussionmentioning

confidence: 99%

An Origami-Inspired Spherical Transformable Metamaterial Based on Symmetry Groups

Nuijts

Broeren

Wijk

et al. 2019

2019 7th International Conference on Control, Mechatronics and Automation (ICCMA)

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An origami inspired spherical transformable metamaterial based on symmetry groups I.R. Nuijts PrefaceThis thesis is the final product of the master Biomechanical Design from the faculty Mechanical, Maritime and Materials Engineering at the Delft University of Technology. I started the bachelor study of Mechanical Engineering in September of 2013. After finishing the bachelor I started with the Mechanical Engineering master, specialisation Biomechanical Design and track Bio-Inspired Technologies. The masters theses from this specialisation were not in line with my interests and so I arrived at High-Tech Engineering where I met Freek Broeren, who was at the time investigating more interesting concepts.I would like to thank Freek Broeren for his weekly feedback and support for almost a year. I would also like to thank Volkert van der Wijk for his constructive feedback and guiding and the supporting staff at the High-Tech Engineering workspace for helping during the fabrication process. Lastly I would like to thank my friends and family for supporting and helping during my whole academic career at TU Delft.

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“…The approach calls on D‐symbols, which can be encoded in different ways. We use “Conway cranks” (or cranks), called “extended Schläfli symbols” by Conway et al ., described in . We enumerate all possible cranks that encode two‐dimensional edge‐2‐transitive tilings with topologies (3,3), (3,4), (4,4), (6,3) and (4,6) (and their duals).…”

Section: D‐theory and Weavingsmentioning

confidence: 99%

A Theoretical Schema for Building Weavings of Nets via Colored Tilings of Two‐Dimensional Spaces and Some Simple Polyhedral, Planar and Three‐Periodic Examples

Thompson

Hyde

2018

Israel Journal of Chemistry

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We analyse two-component "weavings" made of a pair of dual (p,q) and (q,p) nets that undulate on both sides of the sphere, the plane and the hyperbolic plane. Families of weavings are described, sharing a common parent net. The examples describe zero-, two-and three-periodic weavings in three-space. We derive all edge-2-transitive weavings with (p,q) = (3,3), (4,3), (4,4), (4,6) using Delaney-Dress tiling theory, described in detail. The two-dimensional hyperbolic weaving are mapped into (euclidean) three-space to form a pair of catenated crystalline nets. The examples suggest generalisations to other weavings on surfaces, including weavings of filaments. A simple hyperbolic weaving of filaments is derived, analogous to the common warp-andweft filament weaving in the plane. The resulting threeperiodic pattern is related to the molecular-scale weaving in the synthetic COF-505 material synthesized by Liu et al.

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The Symmetries of Things

Cited by 135 publications

References 0 publications

Octulene: A Hyperbolic Molecular Belt that Binds Chloride Anions

Octulene: A Hyperbolic Molecular Belt that Binds Chloride Anions

An Origami-Inspired Spherical Transformable Metamaterial Based on Symmetry Groups

A Theoretical Schema for Building Weavings of Nets via Colored Tilings of Two‐Dimensional Spaces and Some Simple Polyhedral, Planar and Three‐Periodic Examples

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