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Edge Matrix of Hyperbolic Simplices

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Abstract

In this paper, by using the dual problem which was solved by Feng Luo (Geom. Dedicata 64 (1997), 277–282) and a new method, we give necessary and sufficient conditions for given (n(n+1)) /2 positive real numbers to be the edge lengths of a hyperbolic n-simplex. By using determinants, we also give necessary and sufficient conditions for given (n(n+1)) /2 positive real numbers to be the edge lengths of a spherical n-simplex.

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References

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Authors and Affiliations

  1. Department of Mathematics, Arts and Sciences Faculty, Gazi University, 06500, Teknikokullar Ankara, Turkey

    Baki Karliğa

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  1. Baki Karliğa
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Additional information

Mathematics Subject Classifications (2000). 51M04, 51M05, 51M20, 51M25, 52A38, 52A37, 52B10.

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Karliğa, B. Edge Matrix of Hyperbolic Simplices. Geom Dedicata 109, 1–6 (2004). https://doi.org/10.1007/s10711-004-8882-2

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  • DOI: https://doi.org/10.1007/s10711-004-8882-2

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