Carlo H. Séquin and Yifat Amir and Ruta Jawale and Hong Jeon and Alex Romano and Rohan Taori

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2017-114

May 31, 2017

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2017/EECS-2017-114.pdf

Inspired by a piece of artwork by Bente Simonsen at Bridges 2016, we were looking for various ways of making modular polyhedral toroids from the same basic nonahedron building block. Since the chosen building block cannot be an ideal, regular Johnson solid, we used greedy optimization methods, such as gradient descent, to minimize the variations of the edge lengths and the deviations from regular n-gons for the facets of the nonahedron, while maintaining the planarity of the connecting faces for each toroidal configuration. In general, we tried to maximize overall symmetry. Polyhedra with a genus as high as 11 have been constructed using a 3D printer.

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BibTeX citation:

@techreport{Séquin:EECS-2017-114,
    Author= {Séquin, Carlo H. and Amir, Yifat and Jawale, Ruta and Jeon, Hong and Romano, Alex and Taori, Rohan},
    Title= {Modular Toroids Constructed from Nonahedra},
    Year= {2017},
    Month= {May},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2017/EECS-2017-114.html},
    Number= {UCB/EECS-2017-114},
    Abstract= {Inspired by a piece of artwork by Bente Simonsen at Bridges 2016, we were looking for various ways of making modular polyhedral toroids from the same basic nonahedron building block.  Since the chosen building block cannot be an ideal, regular Johnson solid, we used greedy optimization methods, such as gradient descent, to minimize the variations of the edge lengths and the deviations from regular n-gons for the facets of the nonahedron, while maintaining the planarity of the connecting faces for each toroidal configuration.  In general, we tried to maximize overall symmetry.  Polyhedra with a genus as high as 11 have been constructed using a 3D printer.},
}

EndNote citation:

%0 Report
%A Séquin, Carlo H. 
%A Amir, Yifat 
%A Jawale, Ruta 
%A Jeon, Hong 
%A Romano, Alex 
%A Taori, Rohan 
%T Modular Toroids Constructed from Nonahedra
%I EECS Department, University of California, Berkeley
%D 2017
%8 May 31
%@ UCB/EECS-2017-114
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2017/EECS-2017-114.html
%F Séquin:EECS-2017-114