Determining All Universal Tilers
Metric Geometry
2012-10-23 v1 Combinatorics
Abstract
A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra. Based on a selected initial cross-section and by applying the slight-rotating operation suitably, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a triangular prism.
Keywords
Cite
@article{arxiv.1110.1715,
title = {Determining All Universal Tilers},
author = {David G. L. Wang},
journal= {arXiv preprint arXiv:1110.1715},
year = {2012}
}
Comments
18 pages, 12 figures