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Decemmber 2011 Topological relationships in spatial tessellations
Viola Weiss, Richard Cowan
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Adv. in Appl. Probab. 43(4): 963-984 (Decemmber 2011). DOI: 10.1239/aap/1324045694

Abstract

Tessellations of R3 that use convex polyhedral cells to fill the space can be extremely complicated. This is especially so for tessellations which are not `facet-to-facet', that is, for those where the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. Adjacency concepts between neighbouring cells (or between neighbouring cell elements) are not easily formulated when facets do not coincide. In this paper we make the first systematic study of these topological relationships when a tessellation of R3 is not facet-to-facet. The results derived can also be applied to the simpler facet-to-facet case. Our study deals with both random tessellations and deterministic `tilings'. Some new theory for planar tessellations is also given.

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Viola Weiss. Richard Cowan. "Topological relationships in spatial tessellations." Adv. in Appl. Probab. 43 (4) 963 - 984, Decemmber 2011. https://doi.org/10.1239/aap/1324045694

Information

Published: Decemmber 2011
First available in Project Euclid: 16 December 2011

zbMATH: 1238.60017
MathSciNet: MR2867941
Digital Object Identifier: 10.1239/aap/1324045694

Subjects:
Primary: 05B45, 52C17, 60D05
Secondary: 51M20, 52B10, 60G55

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 4 • Decemmber 2011
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