Nonexistence of 2-Reptile Simplices

A simplex S is called an m-reptile if it can be tiled without overlaps by simplices S1,S2,...,Sm that are all congruent and similar to S. The only m-reptile d-simplices that seem to be known for d ≥ 3 have m=kd, k ≥ 2. We prove, using eigenvalues, that there are no 2-reptile simplices of dimensions...

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Bibliographic Details
Published inDiscrete and Computational Geometry pp. 151 - 160
Main Author MATOUSEK, Jiri
Format Book Chapter Conference Proceeding
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
Springer
SeriesLecture Notes in Computer Science
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Characteristic Polynomial
Computer science; control theory; systems
Eigenvalue Condition
Exact sciences and technology
Receive Packet
Single Cycle
Theoretical Computer Science
Theoretical computing
Computational geometry
Eigenvalue problem
Probabilistic approach
Modeling
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Summary:A simplex S is called an m-reptile if it can be tiled without overlaps by simplices S1,S2,...,Sm that are all congruent and similar to S. The only m-reptile d-simplices that seem to be known for d ≥ 3 have m=kd, k ≥ 2. We prove, using eigenvalues, that there are no 2-reptile simplices of dimensions d ≥ 3. This investigation has been motivated by a probabilistic packet marking problem in theoretical computer science, introduced by Adler in 2002.
ISBN:3540304673
9783540304678
ISSN:0302-9743
1611-3349
DOI:10.1007/11589440_16