Interlinked Isohedral Tilings of 3D Space

نویسندگان

  • Roman Fuchs
  • Carlo H. Séquin
چکیده

Di erent isohedral tilings of the Euclidian Space are studied in this paper. Using the Voronoi zone in various lattices, we derived toroidal shapes that interlink with each other to ll space completely. The tile of main interest was the 3-segment ring-tile, for which we found several linear approximations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Intricate Isohedral Tilings of 3D Euclidean Space

Various methods to create intricate tilings of 3D space are presented. They include modulated extrusions of 2D Escher tilings, free-form deformations of the fundamental domain of various 3D symmetry groups, highly symmetrical polyhedral toroids of genus 1, higher-genus cage structures derived from the cubic lattice as well as from the diamond and triamond lattices, and finally interlinked tiles...

متن کامل

CAD Tools for Creating Space-filing 3D Escher Tiles

We discuss the design and implementation of CAD tools for creating decorative solids that tile 3-space in a regular, isohedral manner. Starting with the simplest case of extruded 2D tilings, we describe geometric algorithms used for maintaining boundary representations of 3D tiles, including a Java implementation of an interactive constrained Delaunay triangulation library and a mesh-cutting al...

متن کامل

CAD Tools for Creating Space-filling 3D Escher Tiles

We discuss the design and implementation of CAD tools for creating decorative solids that tile 3-space in a regular, isohedral manner. Isohedral tilings of the plane, as popularized by M. C. Escher, can be constructed by hand or using existing tools on the web. Specialized CAD tools have also been developed for tiling other 2-manifolds. This work addresses the question: How can we generate inte...

متن کامل

Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry

We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There are no isohedral tilings with p3m1, p4m, or p6m symmetry groups that have polyominoes or polyiamonds...

متن کامل

Fundamental Domains of Discrete Groups Acting on Euclidean Space

Fundamenatal domains of wallpaper groups acting on R2 whose closures are homeomorphic to closed disks can be classified in the same way that Grunbaum classifies isohedral plane tilings in [7]. Almost all of these types of fundamental domains appear as Dirichlet domains, and examples are given.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008