Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Interlinked Isohedral Tilings of 3D Space

Roman Fuchs and Carlo H. Séquin

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2008-83
June 30, 2008

http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-83.pdf

This work studies the generation of simple interlinked isohedral tilings of Euclidian Space. We start from interlinked wire frames derived from 3D lattices of high symmetry, in particular, the cubic lattice, the diamond lattice, and the triamond lattice. Forming the Voronoi regions around the original regular arrays of wire frames, we derived toroidal shapes with a small number of planar facets that interlink with each other to fill 3D space completely. The main focus was on a 3-segment ring-tile, derived from the symmetries of the triamond lattice; several simple and pleasing linear approximations have been found.


BibTeX citation:

@techreport{Fuchs:EECS-2008-83,
    Author = {Fuchs, Roman and Séquin, Carlo H.},
    Title = {Interlinked Isohedral Tilings of 3D Space},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2008},
    Month = {Jun},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-83.html},
    Number = {UCB/EECS-2008-83},
    Abstract = {This work studies the generation of simple interlinked isohedral tilings of Euclidian Space. We start from interlinked wire frames derived from 3D lattices of high symmetry, in particular, the cubic lattice, the diamond lattice, and the triamond lattice. Forming the Voronoi regions around the original regular arrays of wire frames, we derived toroidal shapes with a small number of planar facets that interlink with each other to fill 3D space completely. The main focus was on a 3-segment ring-tile, derived from the symmetries of the triamond lattice;  several simple and pleasing linear approximations have been found.}
}

EndNote citation:

%0 Report
%A Fuchs, Roman
%A Séquin, Carlo H.
%T Interlinked Isohedral Tilings of 3D Space
%I EECS Department, University of California, Berkeley
%D 2008
%8 June 30
%@ UCB/EECS-2008-83
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-83.html
%F Fuchs:EECS-2008-83