Rhombic embeddings of planar quad-graphs

被引：58

作者：

Kenyon, R ^{[1
]}

Schlenker, JM

机构：

[1] Univ Paris 11, Math Lab, CNRS, UMR 8628, F-91405 Orsay, France

[2] Univ Toulouse 3, Inst Math, Lab Emile Picard, CNRS,UMR 5580, F-31062 Toulouse, France

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 357卷 / 09期

关键词：

D O I：

10.1090/S0002-9947-04-03545-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a finite or infinite planar graph all of whose faces have degree 4, we study embeddings in the plane in which all edges have length 1, that is, in which every face is a rhombus. We give a necessary and sufficient condition for the existence of such an embedding, as well as a description of the set of all such embeddings.

引用

页码：3443 / 3458

页数：16