On the space-filling enneahedra

M. Goldberg

DOI:10.1007/BF00147314
Corpus ID: 120914105

On the space-filling enneahedra

@article{Goldberg1982OnTS,
  title={On the space-filling enneahedra},
  author={Michael Goldberg},
  journal={Geometriae Dedicata},
  year={1982},
  volume={12},
  pages={297-306}
}

M. Goldberg
Published 1 June 1982
Physics
Geometriae Dedicata

A space-filling polyhedron is one whose replications can be packed to fill three-space completely. The space-filling polyhedra of four to eight faces have been previously reported. The search is here extended to the convex space-fillers of nine faces. The number of types is found to be at least 40.

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5 Citations

Background Citations

Surface-area-minimizing n-hedral Tiles

We provide a list of conjectured surface-area-minimizing n-hedral tiles of space for n from 4 to 14, previously known only for n equal to 5 or 6. We find the optimal "orientation-preserving"…

Space Filling Delaunay Loft Sculptures

atthewNgRgunKlémanTexas.
Computer Science
2019

A generalized procedure for generating space filling shapes is developed, which is called Delaunay Lofts — a new class of scutoid-like shapes inspired by “scutoids” — shapes that were recently reported to occur in epithelial cells due to topological changes between the extremal (apical and basal) surfaces of epithelia.

Delaunay Lofts: A biologically inspired approach for modeling space filling modular structures

S. SubramanianM. EngVinayak R. KrishnamurthyE. Akleman
Computer Science
Comput. Graph.
2019

Generative Infills for Additive Manufacturing Using Space-Filling Polygonal Tiles

M. EbertS. SubramanianE. AklemanVinayak R. Krishnamurthy
Mathematics
Volume 11B: 46th Design Automation Conference (DAC)
2020

A simple yet powerful geometric modeling framework that combines the idea of Voronoi decomposition space with wallpaper symmetries defined in 2-space to generate wallpaper-infills for additive manufacturing based on space-filling shapes is presented.

Bi-Axial Woven Tiles: Interlocking Space-Filling Shapes Based on Symmetries of Bi-Axial Weaving Patterns

Vinayak R. KrishnamurthyE. Akleman N Yadav
Computer Science
Graphics Interface
2020

This paper introduces a geometric design and fabrication framework for a family of interlocking space-filling shapes called bi-axial woven tiles based on a unique combination of Voronoi partitioning of space using curve segments as the Voronoa sites and the design of these curve segments based on weave patterns closed under symmetry operations.

References

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On the space-filling heptahedra

M. Goldberg
Geology
1977

A space-filling polyhedron is one whose replications can be packed to fill three-space completely. The space-filling tetrahedra, pentahedra and hexahedra have been previously investigated. The search…