Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delambre-Gauss Formulas for Augmented, Right-Angled Hexagons in
  Hyperbolic 4-Space   We study the geometry of oriented right-angled hexagons in H^4, the
hyperbolic 4-space, via Clifford numbers or quaternions. We show how to augment
alternate sides of such a hexagon so that for the non-augmented sides, we can
define quaternion half side-lengths whose angular parts are obtained from half
the Euler angles associated to a certain orientation-preserving isometry of the
Euclidean 3-space. This generalizes the complex half side-lengths of oriented
right-angled hexagons in H^3. We also define appropriate complex half
side-lengths for the augmented sides of the hexagon. We further explain how to
geometrically read off the quaternion half side-lengths for a given
oriented,augmented, right-angled hexagon in H^4. Our main result is a set of
generalized Delambre-Gauss formulas for oriented, augmented, right-angled
hexagons in H^4, involving the quaternion half side-lengths and the complex
half side-lengths. We also show in the appendix how the same method gives
Delambre-Gauss formulas for oriented right-angled hexagons in H^3, from which
the well-known sine and cosine laws can be deduced. These formulas generalize
the classical Delambre-Gauss formulas for spherical/hyperbolic triangles.

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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex