Document Type
Conference Proceeding
Publication Date
1-1-2008
Publication Title
Computational Geometry: Theory and Applications
Abstract
We investigate a question initiated in the work of Sibley and Wagon, who proved that 3 colors suffice to color any collection of 2D parallelograms glued edge-to-edge. Their proof relied on the existence of an "elbow" parallelogram. We explore the existence of analogous "corner" parallelepipeds in 3D objects. Our results are twofold. First, we refine the 2D proof to render information on the number and location of the 2D elbows. Second, we prove that not all of the 2D refinements extend to 3D.
Keywords
Brick, Coloring, Corner, Elbow, Parallelepiped, Parallelogram
Volume
39
Issue
1
First Page
43
Last Page
54
DOI
10.1016/j.comgeo.2007.05.010
ISSN
09257721
Rights
© 2007 Elsevier B.V.
Recommended Citation
Damian, Mirela and O'Rourke, Joseph, "On Corners of Objects Built from Parallelepiped Bricks" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/191
Comments
Archived as published. Open access paper.