Abstract
A convexd-polytype inE d is called semiregular, if its facets are regular and its vertices equivalent. A list of semiregular polytopes ford≥4 is known since 1900. Recently it has been proved by П. В. Макаров [сб. Вопр. дискр. геом., Мат. исслед. ИМ АН Молд. ССР вып. 103, C. 139–150, Кищинев 1988], that this list is complete ford=4. We present here a simple proof for that this list is complete in any dimension.
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Blind, G., Blind, R. The semiregular polytopes. Comment. Math. Helv. 66, 150–154 (1991). https://doi.org/10.1007/BF02566640
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DOI: https://doi.org/10.1007/BF02566640