Geodesic
Ideal Uniform Polyhedra in $\mathbb{H}^{n}$ and Covolumes of Higher Dimensional Modular Groups
Canadian journal of mathematics, Tome 73 (2021) no. 2, pp. 465-492

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DOI

Higher dimensional analogues of the modular group $\mathit{PSL}(2,\mathbb{Z})$ are closely related to hyperbolic reflection groups and Coxeter polyhedra with big symmetry groups. In this context, we develop a theory and dissection properties of ideal hyperbolic $k$-rectified regular polyhedra, which is of independent interest. As an application, we can identify the covolumes of the quaternionic modular groups with certain explicit rational multiples of the Riemann zeta value $\unicode[STIX]{x1D701}(3)$.
DOI : 10.4153/S0008414X20000036
Mots-clés : Ideal hyperbolic polyhedron, k-rectification, Napier cycle, Coxeter group, quaternionic modular group, hyperbolic volume, zeta value 
Kellerhals, Ruth. Ideal Uniform Polyhedra in $\mathbb{H}^{n}$ and Covolumes of Higher Dimensional Modular Groups. Canadian journal of mathematics, Tome 73 (2021) no. 2, pp. 465-492. doi: 10.4153/S0008414X20000036
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     title = {Ideal {Uniform} {Polyhedra} in $\mathbb{H}^{n}$ and {Covolumes} of {Higher} {Dimensional} {Modular} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {465--492},
     year = {2021},
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     doi = {10.4153/S0008414X20000036},
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