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The author wishes to thank Professor R. Schneider for helpful discussion, especially for referring his attention to the useful notionincluded double cone.
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Martini, H. A new view on some characterizations of simplices. Arch. Math 55, 389–393 (1990). https://doi.org/10.1007/BF01198479
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DOI: https://doi.org/10.1007/BF01198479