A144222 Floor of the volumes of the first sixteen Lobell polyhedra.

4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24

Offset

5,1

Comments

This article defines a pair of combinatorial operations on the combinatorial structure of compact right-angled hyperbolic polyhedra in dimension three called decomposition and edge surgery. It is shown that these operations simplify the combinatorics of such a polyhedron, while keeping it within the class of right-angled objects, until it is a disjoint union of Lobell polyhedra, a class of polyhedra which generalizes the dodecahedron. Furthermore, these combinatorial operations are shown to have geometric realizations which are volume decreasing. This allows for an organization of the volumes of right-angled hyperbolic polyhedra and allows, in particular, the determination of the polyhedra with smallest and second-smallest volumes.

Links

Table of n, a(n) for n=5..20.

Taiyo Inoue, Organizing Volumes of Right-Angled Hyperbolic Polyhedra, arXiv:0809.2111 [math.GT]

Formula

a(n) = Floor[vol(L(n))].

Example

n..|.vol(L(n))
==============
5..|.4.306....
6..|.6.023....
7..|.7.563....
8..|.9.019....
9..|10.426....
10.|11.801....
11.|13.156....
12.|14.494....
13.|15.822....
14.|17.140....
15.|18.452....
16.|19.758....
17.|21.059....
18.|22.356....
19.|23.651....
20.|24.943....
==============

Crossrefs

Sequence in context: A001690 A105447 A242286 * A010414 A254122 A095096

Adjacent sequences: A144219 A144220 A144221 * A144223 A144224 A144225

Keyword

nonn

Author

Jonathan Vos Post, Sep 14 2008

Extensions

Replaced link to cached arXiv URL by the permanent version - R. J. Mathar, Mar 01 2010

Status

approved