## Abstract

Let T be a triangulation of a closed topological cube Q, and let V be the set of vertices of T. Further assume that the triangulation satisfies a technical condition which we call the triple intersection property (see Definition 3.6). Then there is an essentially unique tiling C={Cv:v∈V} of a rectangular parallelepiped R by cubes, such that for every edge (u,v) of T the corresponding cubes Cv, C _{u} have nonempty intersection, and such that the vertices corresponding to the cubes at the corners of R are at the corners of Q. Moreover, the sizes of the cubes are obtained as a solution of a variational problem which is a discrete version of the notion of extremal length in R ^{3}.

Original language | English |
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Pages (from-to) | 2795-2805 |

Number of pages | 11 |

Journal | Topology and its Applications |

Volume | 159 |

Issue number | 10-11 |

DOIs | |

State | Published - 15 Jun 2012 |

Externally published | Yes |

## Keywords

- Discrete conformal geometry
- Extremal length
- Tiling by cubes

## ASJC Scopus subject areas

- Geometry and Topology