volume 30, issue 2, P343-353 2003
DOI: 10.1007/s00454-003-0015-6
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Abstract: Let S d be a d-dimensional simplex in R d , and let H be an affine hyperplane of R d . We say that H is a medial hyperplane of S d if the distance between H and any vertex of S d is the same constant. The intersection of S d and a medial hyperplane is called a medial section of S d . In this paper we give a simple formula for the (d − 1)-volume of any medial section of S d in terms of the lengths of the edges of S d . This extends the result of Yetter [5] from the three-dimensional case to arbitrary dimension…

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