volume 31, issue 3, P421-433 2004
DOI: 10.1007/s00454-003-2907-8
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Abstract: We construct two classes of wildly embedded space fillers of R 3 . First, every crumpled cube is shown to have an embedding in R 3 that admits a monohedral tiling of R 3 . Second, a solid Alexander horned sphere with a topologically trivial interior is shown to admit a monohedral tiling of a cube and hence R 3 . By joining a solid horned sphere with compact polyhedral 3-submanifolds of R 3 with one boundary component, we construct space fillers homeomorphic to the polyhedral submanifolds but of different embe…

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