Visualizing hyperbolic honeycombs
نویسندگان
چکیده
منابع مشابه
Regular Honeycombs in Hyperbolic Space
made a study of honeycombs whose cells are equal regular polytopes in spaces of positive, zero, and negative curvature. The spherical and Euclidean honeycombs had already been described by Schlaf li (1855), but the only earlier mention of the hyperbolic honeycombs was when Stringham (1880, pp. 7, 12, and errata) discarded them as "imaginary figures", or, for the two-dimensional case, when Klein...
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Small and large deformation in-plane elastic response of a new class of hierarchical fractal-like honeycombs inspired by the topology of the ''spiderweb'' were investigated through analytical modeling, detailed numerical simulations, and mechanical testing. Small deformation elasticity results show that the isotropic in-plane elastic moduli (Young's modulus and Poisson's ratio) of the structure...
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A new class of hierarchical fractal-like honeycombs inspired by the topology of the “spiderweb” were introduced and their small and large deformations were investigated analytically, numerically, and experimentally. Small deformation elasticity results show that the isotropic in-plane elastic moduli (Young’s modulus and Poisson’s ratio) of the structures can be controlled over several orders of...
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In a former paper [18] a method is described that determines the data and the density of the optimal ball or horoball packing to each Coxeter tiling in the hyperbolic 3-space. In this work we extend this procedure – based on the projective interpretation of the hyperbolic geometry – to higher dimensional Coxeter honeycombs in H, (d = 4, 5), and determine the metric data of their optimal ball an...
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ژورنال
عنوان ژورنال: Journal of Mathematics and the Arts
سال: 2017
ISSN: 1751-3472,1751-3480
DOI: 10.1080/17513472.2016.1263789