Geodesic
A Counterexample to a Classification Theorem of Linearly Stable Polytopes
Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 92-93

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We give an example of a centrally symmetric 5-polytope which is linearly stable though its vertices do not form a subset of the vertices of a 5-cube. This example contradicts the “only if” part of the classification theorem on linearly stable poly topes stated by P. McMullen [2]. Moreover the example gives a 5-polytope, the vertices of which form a subset of a 5-cube while its dual does not possess the same property. 
Assaf, David. A Counterexample to a Classification Theorem of Linearly Stable Polytopes. Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 92-93. doi: 10.4153/CJM-1976-010-9
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[1] 1. Grunbaum, B., Convex polytopes (Wiley, New York, 1967). Google Scholar

[2] 2. McMullen, P., Linearly stable polytopes, Can. J. Math., 21 (1969), 1427–1431. Google Scholar

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