Abstract
In [7] S. K. Stein constructed a 10-dimensional centrally-symmetric star body whose translates tile 10 10 -space but whose translates by a lattice do not tile it. In [8] he constructed a 5 5 -dimensional star polyhedron whose translates tile 5 5 -space but whose congruent copies by a group of motions do not tile it. So there is no lattice tiling by translates of this polyhedron. In the present paper we shall construct a 5 5 -dimensional centrally-symmetric star polyhedron whose translates tile 5 5 -space but whose congruent copies by a group of motions do not tile it. Furthermore, this phenomenon occurs at an infinitude of dimensions.
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