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From 2D Hyperbolic Forests to 3D Euclidean Entangled Thickets

Hyde, Stephen; Oguey, Christophe

Description

A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P, D, gyroid and H surfaces. Some of these graphs are natural generalisations of bicontinuous topologies to bi-, tri-, quadra-and octa-continuous forms. Interwoven...[Show more]

CollectionsANU Research Publications
Date published: 2000
Type: Journal article
URI: http://hdl.handle.net/1885/89039
Source: European Physical Journal B

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