Enumeration of lattice 3-polytopes with few lattice points
This is the data page accompanying the paper
Update, April 2021:
These data has been extended up to 15 lattice points (computed via polymake) and incorporated in searchable form to the polymake database, mantained by Andreas Paffenholz.
To access the database go to https://polydb.org and in the "List of collections" select "Polytopes" -> "Lattice Polytopes" -> "3d-Lattice Polytopes with Few Lattice Points".
The following files contain the full lists of
lattice 3-polytopes of width larger than one and size (=total
number of lattice points) up to eleven.
Details on the algorithm used and the theoretical justification for it can be found in the above referenced paper,
and in Mónica Blanco's Ph.D. thesis.
The Appendix in the thesis contains implementation details, including all the code, in MATLAB.
For each size, "properties" links to a zipped folder containing one .txt file for each polytope, with a list of properties of it;
"latticepoints" links to a .txt file with all the polytopes of that size, each given as a list of its lattice points. (In sizes 10 and 11 the file
is divided into several parts, with at most 10.000 polytopes each).
To DOWNLOAD, click right button on link and "Save link
as..."
- Size 5 (9 polytopes):
properties, latticepoints
- Size 6 (76 polytopes):
properties,
latticepoints
- Size 7 (496
polytopes):
properties,
latticepoints
- Size 8 (2675
polytopes):
properties,
latticepoints
- Size 9 (11698
polytopes): properties,
latticepoints
- Size 10 (45035
polytopes): properties,
latticepoints (1,
2,
3,
4,
5)
- Size 11 (156464
polytopes): properties,
latticepoints (1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16)