Simplices with equiareal faces

Details Simplices with equiareal faces Simplices with equiareal faces

2009-09-10

arxiv.org/abs/0909.1859v1

Mathematics

Metric Geometry

6 pages, 2 figures

Scientific paper

We study simplices with equiareal faces in the Euclidean 3-space by means of
elementary geometry. We present an unexpectedly simple proof of the fact that,
if such a simplex is non-degenerate, than every two of its faces are congruent.
We show also that this statement is wrong for degenerate simplices and find all
degenerate simplices with equiareal faces.

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