Abstract
A somewhat fundamental sequence of antiprisms is defined, the d-th antiprism having dimension d, each being a base of the next. The f-vectors of these polytopes are determined. In particular, it is shown that the number of faces of the d-th antiprism is the number of partitions of \(2^{d+1}\) into powers of 2. In order to better understand the structure of the face lattices of these polytopes and their interrelationship, it is convenient also to introduce a countably infinite lattice, the elements of which correspond to the partitions of powers of 2 into powers of 2. This lattice has the property that it is isomorphic to its lattice of intervals, and it is the smallest such lattice.
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The paper benefited from comments of Elie Alhajjar, George Andrews, Michael Dobbins, and an unknown referee.
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Lawrence, J. Dual-Antiprisms and Partitions of Powers of 2 into Powers of 2. Discrete Comput Geom 61, 465–478 (2019). https://doi.org/10.1007/s00454-019-00070-5
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DOI: https://doi.org/10.1007/s00454-019-00070-5