On corners of objects built from parallelepiped bricks

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چکیده

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On corners of objects built from parallelepiped bricks

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, which would lead to 4-coloring. Our results are threefold. First, we refine the 2D proo...

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We address a question posed by T. Sibley and Stan Wagon. They proved that rhombic Penrose tilings in the plane can be 3-colored, but a key lemma of their proof fails in the natural 3D generalization. In that generalization, an object is built from bricks, each of which is a parellelopiped, and they are glued face-toface. The question is: How many colors are needed to color the bricks of any suc...

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ژورنال

عنوان ژورنال: Computational Geometry

سال: 2008

ISSN: 0925-7721

DOI: 10.1016/j.comgeo.2007.05.010