

A144222


Floor of the volumes of the first sixteen Lobell polyhedra.


2



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

5,1


COMMENTS

This article defines a pair of combinatorial operations on the combinatorial structure of compact rightangled 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 rightangled 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 rightangled hyperbolic polyhedra and allows, in particular, the determination of the polyhedra with smallest and secondsmallest volumes.


LINKS

Table of n, a(n) for n=5..20.
Taiyo Inoue, Organizing Volumes of RightAngled 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



