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The volume of a compact hyperbolic antiprism. / Abrosimov, Nikolay; Vuong, Bao.

In: Journal of Knot Theory and its Ramifications, Vol. 27, No. 13, 1842010, 11.2018.

Research output: Contribution to journal › Article › peer-review

Harvard

Abrosimov, N & Vuong, B 2018, 'The volume of a compact hyperbolic antiprism', Journal of Knot Theory and its Ramifications, vol. 27, no. 13, 1842010. https://doi.org/10.1142/S0218216518420105

APA

Abrosimov, N., & Vuong, B. (2018). The volume of a compact hyperbolic antiprism. Journal of Knot Theory and its Ramifications, 27(13), [1842010]. https://doi.org/10.1142/S0218216518420105

Vancouver

Abrosimov N, Vuong B. The volume of a compact hyperbolic antiprism. Journal of Knot Theory and its Ramifications. 2018 Nov;27(13):1842010. doi: 10.1142/S0218216518420105

Author

Abrosimov, Nikolay ; Vuong, Bao. / The volume of a compact hyperbolic antiprism. In: Journal of Knot Theory and its Ramifications. 2018 ; Vol. 27, No. 13.

BibTeX

@article{74bcff49f8a343faa7b9de5795d7e84a,
title = "The volume of a compact hyperbolic antiprism",
abstract = "We consider a compact hyperbolic antiprism. It is a convex polyhedron with 2n vertices in the hyperbolic space H3. This polyhedron has a symmetry group S2n generated by a mirror-rotational symmetry of order 2n, i.e. rotation to the angle π/n followed by a reflection. We establish necessary and sufficient conditions for the existence of such polyhedra in H3. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formulas expressing the volume of a hyperbolic antiprism in terms of the edge lengths.",
keywords = "Compact hyperbolic antiprism, hyperbolic volume, rotation followed by reflection, symmetry group S 2 n, symmetry group S n, symmetry group S-2n",
author = "Nikolay Abrosimov and Bao Vuong",
year = "2018",
month = nov,
doi = "10.1142/S0218216518420105",
language = "English",
volume = "27",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "13",

}

RIS

TY - JOUR

T1 - The volume of a compact hyperbolic antiprism

AU - Abrosimov, Nikolay

AU - Vuong, Bao

PY - 2018/11

Y1 - 2018/11

N2 - We consider a compact hyperbolic antiprism. It is a convex polyhedron with 2n vertices in the hyperbolic space H3. This polyhedron has a symmetry group S2n generated by a mirror-rotational symmetry of order 2n, i.e. rotation to the angle π/n followed by a reflection. We establish necessary and sufficient conditions for the existence of such polyhedra in H3. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formulas expressing the volume of a hyperbolic antiprism in terms of the edge lengths.

AB - We consider a compact hyperbolic antiprism. It is a convex polyhedron with 2n vertices in the hyperbolic space H3. This polyhedron has a symmetry group S2n generated by a mirror-rotational symmetry of order 2n, i.e. rotation to the angle π/n followed by a reflection. We establish necessary and sufficient conditions for the existence of such polyhedra in H3. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formulas expressing the volume of a hyperbolic antiprism in terms of the edge lengths.

KW - Compact hyperbolic antiprism

KW - hyperbolic volume

KW - rotation followed by reflection

KW - symmetry group S 2 n

KW - symmetry group S n

KW - symmetry group S-2n

UR - http://www.scopus.com/inward/record.url?scp=85057366934&partnerID=8YFLogxK

U2 - 10.1142/S0218216518420105

DO - 10.1142/S0218216518420105

M3 - Article

AN - SCOPUS:85057366934

VL - 27

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 13

M1 - 1842010

ER -

ID: 17687441