TY - JOUR
T1 - The number of cusps of right-angled polyhedra in hyperbolic spaces
AU - Nonaka, Jun
PY - 2015/12
Y1 - 2015/12
N2 - As was pointed out by Nikulin [8] and Vinberg [10], a right-angled polyhedron of finite volume in the hyperbolic n-space Hn has at least one cusp for n ≥ 5. We obtain non-trivial lower bounds on the number of cusps of such polyhedra. For example, right-angled polyhedra of finite volume must have at least three cusps for n = 6. Our theorem also says that the higher the dimension of a right-angled polyhedron becomes, the more cusps it must have.
AB - As was pointed out by Nikulin [8] and Vinberg [10], a right-angled polyhedron of finite volume in the hyperbolic n-space Hn has at least one cusp for n ≥ 5. We obtain non-trivial lower bounds on the number of cusps of such polyhedra. For example, right-angled polyhedra of finite volume must have at least three cusps for n = 6. Our theorem also says that the higher the dimension of a right-angled polyhedron becomes, the more cusps it must have.
KW - Combinatorics
KW - Cusp
KW - Hyperbolic space
KW - Right-angled polyhedron
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U2 - 10.3836/tjm/1452806056
DO - 10.3836/tjm/1452806056
M3 - Article
AN - SCOPUS:84981340932
SN - 0387-3870
VL - 38
SP - 539
EP - 560
JO - Tokyo Journal of Mathematics
JF - Tokyo Journal of Mathematics
IS - 2
ER -