We show that any triangulation of the 5-cube I5 by complete truncation, i.e., "slicing off" the even (or the odd) vertices, cannot use less than 67 or more than 68 pieces.
Broadie, Mark, and Richard Cottle. "A note on triangulating the 5-cube." Discrete Mathematics 52, no. 1 (1984): 39-49.
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