Nexus Network Journal

, Volume 15, Issue 2, pp 241–255 | Cite as

Structures of Periodical Knots and Links as Geometric Models of Complex Surfaces for Designing



Practical modeling of spatial surfaces is more convenient by means of transformation of their flat developments made as topologically connected kinetic structures. Topologically, any surface in 3D space consists of three types of elements: planar facets, linear edges and point vertexes. Planar facets and linear edges can be identifed respectively with the structural units of folding structures and kinematical nets. Here we consider a third possible type of flat transformable structures with vertexes as form-generative units, in which flat developments of surfaces are formed by arranged point sets given by contacting crossing points of the periodic knots and links made of elastic-flexible materials, so that their crossing points have real physical contacts. This new form-generative method can be applied to modeling of both oriented and non-oriented differentiable topological 2D manifolds. The method of form generation based upon the developing properties of periodic structures of knots and links may be applied to many practical fields, including art, design and architecture.


modeling design theory domes surfaces topology kinetic structures folding structures kinematical nets periodic structures knots links 


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Copyright information

© Kim Williams Books, Turin 2013

Authors and Affiliations

  1. 1.Research Institute of Theory and History of Architecture and Town-planningRussian Academy of the Architecture and Construction SciencesMoscowRussia

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