FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 4, PAGES 203-211

Wild tiles in R3 with spherical boundaries

T.-M. Tang

Abstract

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Wildly embedded tiles in R3 with spherical boundary are discussed. The construction of the topologically complicated, crumpled cube tiles is reviewed. We construct an infinite family of wildly embedded, cellular tiles with Fox--Artin-type wild points. Finally, a condition on the set of wild points on a cellular tile is given to show that certain wild cells cannot be tiles. Several observations are recorded for further investigations.

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