Abstract
We exhibit a nonregular triangulation for the product of two tetrahedra. This answers a question by Gel'fand, Kapranov, and Zelevinsky. We also give a complete classification of the symmetry classes of regular triangulations of ▽2×▽3. Our nonregular triangulation of ▽3×▽3 can be extended to a nonregular triangulation of the six-dimensional cube. The four-dimensional cube is the smallest cube with a nonregular triangulation.
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This research was partially supported by a doctoral fellowship of the National University of Mexico, the National Science Foundation, and the David and Lucile Packard Foundation.
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de Loera, J.A. Nonregular triangulations of products of simplices. Discrete Comput Geom 15, 253–264 (1996). https://doi.org/10.1007/BF02711494
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DOI: https://doi.org/10.1007/BF02711494