Fabricable dihedral Escher tessellations

Xiaokang Liu, Lin Lu*, Andrei Sharf, Xin Yan, Dani Lischinski, Changhe Tu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The growing popularity of 3D digital manufacturing has spurred a high demand for accessible methods for designing and fabricating customized 3D objects. In this paper, we present a novel approach to model and fabricate Escher dual-shape tilings from user-defined shapes. In a nutshell, Escher's dual shape tiling method smoothly transforms one tile pattern into another, generating a dual perception effect of the two shapes. We adapt Escher's dual shape tiling and perception effect to 3D manufacturing. Thus, our method takes two user-defined shapes and computes their dual shape tiling. A key feature of our method is that the dual shape patterns utilize solid and hollow spaces simultaneously. Specifically, our technique maps one shape to solid structure, while the second shape is mapped to hollow background, optimizing both spaces and bringing higher utilization of materials. To conform with 3D printability requirements, our tiling computation accounts for connectivity and strength as well as dense packing for efficiency. Our dual shape tiling algorithm gives rise to novel manufacturing applications such as ornamental texturing with dual perception Escher patterns, decorative window blinds, flexible tiling patterns, and shade effects.

Original languageAmerican English
Article number102853
JournalCAD Computer Aided Design
StatePublished - Oct 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Ltd


  • Digital fabrication
  • Dihedral tessellation
  • Shape modeling


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