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Reviewed by Suhyoung Choi References

By Mohanty Yana (-ucsd, Y. Cho, H. Kim and Discrete Comput Geom


Construction of a 3/4-ideal hyperbolic tetrahedron out of ideal tetrahedra. (English summary) Discrete Comput. Geom. 32 (2004), no. 1, 117–128. This paper gives a useful straightforward formula for computing volumes of finite tetrahedra in the hyperbolic space. First the author expresses the volume of a finite tetrahedron in terms of the volumes of ideal tetrahedra and 3/4-ideal tetrahedra. Then a 3/4-ideal tetrahedron is constructed out of 10 ideal tetrahedra. The scissors congruence plays an important role here. This is an improvement on the earlier work of Y. Cho and H. Kim [Discrete Comput. Geom. 22 (1999), no. 3, 347–366; MR1706606 (2000k:52008)]

Topics: 10. C.-H. Sah, Scissors congruences, I, Gauss–Bonnet map, Math. Scand. 49 (1982, 181–210. MR0661890 (84b, 53062a) 11. E. B. Vinberg, Volumes of non-Euclidean polyhedra, Russian Math. Surveys 48(2) (1993
Year: 2013
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