# GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE

• Cho, Yunhi ;
• Kim, Hyuk
• Published : 2013.11.01
• 68 9

#### Abstract

We give a geometric proof of the analyticity of the volume of a tetrahedron in extended hyperbolic space, when vertices of the tetrahedron move continuously from inside to outside of a hyperbolic space keeping every face of the tetrahedron intersecting the hyperbolic space. Then we find a geometric and analytic interpretation of a truncated orthoscheme and Lambert cube in the hyperbolic space from the viewpoint of a tetrahedron in the extended hyperbolic space.

#### Keywords

hyperbolic space;volume;analytic continuation

#### References

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#### Cited by

1. Combinatorial Decompositions, Kirillov–Reshetikhin Invariants, and the Volume Conjecture for Hyperbolic Polyhedra 2016, https://doi.org/10.1080/10586458.2016.1242441

#### Acknowledgement

Supported by : Korea Research Foundation(KRF)