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Simplexes in spaces of constant curvature

✍ Scribed by B. V. Dekster; J. B. Wilker


Publisher
Springer
Year
1991
Tongue
English
Weight
543 KB
Volume
38
Category
Article
ISSN
0046-5755

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✦ Synopsis


In hyperbolic, Euclidean and spherical n-space, we determine, for each positive number l, the largest interval of the form ),.(/) ~< l u ~< l which guarantees the existence of an nsimplex Pl P2 "'" P,+t with edge-lengths pipj=lu. (In spherical geometry of curvature 1 the interval is empty unless 1 ~< 2 arcsin ~.)

The assertion that these intervals are as large as possible is justified because each of them allows certain degenerate simplexes. We determine explicitly all of these critical configurations.


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