Census of Rotary Maps by Genus and Number of Edges

During a workshop on Symmetries of discrete structures in Kranjska Gora in 2022, Marston Conder suggested that it would be worth extending his census of rotary maps of small genus (that went up to genus 301). To do that, an extension of the census of rotary maps on up to 1500/3000 edges in the non-orientable/orientable case (constructed by Pablo Spiga, Gabriel Verret and Primož Potočnik in 2014) would be useful. Using the same mathematical ideas, but improving and optimising some of the algorithms, we obtained a complete list of rotary maps (both chiral as well as fully regular) on up to 6000 edges in the orientable case, and up to 3000 edges in the non-orientable case. With some extra work (dealing with the maps of some particular valencies and face-lengths), we obtained all rotary maps on surfaces of genus up to 1501 in the orientable case and up to 1502 in the non-orientable case.

Census by genus

Some basic information about the rotary maps of these genera are stored in the excel files below (see here for the explanation of the column labels):

• Excel spreadsheet of chiral maps of genus between 2 and 1501 (8.8MB)
• Excel spreadsheet of regular orientable maps of genus between 2 and 1501 (34.7MB)
• Excel spreadsheet of regular non-orientable maps of genus between 3 and 1502 (2.2MB)

The actual maps are given as a magma package, which is available for download as a zipped file (12 MB). The functionalities of the magma package are described in a text file.

Census by the number of edges

The information of all rotary maps with at least 2 and at most 3000 edges will soon become available here.
Some basic information about the rotary maps with at least 2 and at most 3000 edges (at most 6000 edges in the orientable case) are stored in the excel files below (see here for the explanation of the column labels):

• Excel spreadsheet of fully regular maps with at least 2 and at most 3000 edges (30.9 MB)
• Excel spreadsheet of chiral maps with at least 2 and at most 6000 edges (46.1 MB)
• Excel spreadsheet of large regular orientable maps with at least 3001 and at most 6000 edges (22.4 MB)

The actual maps are given as magma packages, which are available for download as zipped files at the following links:

• Fully regular maps with at least 2 and at most 3000 edges (11.2 MB)
• Chiral maps with at least 2 and at most 6000 edges (18.9 MB)
• Large regular orientable maps with at least 3001 and at most 6000 edges. This zipped file contains also a magma package with all 2*-groups of order at most 12000 (3.88 GB)

The functionalities of the magma package are described in this file.

Census of the skeletons

We have also computed the skeletons (underlying graphs) of all rotary maps having at most 3000 edges. We provide two separate excel files for the skeletons of all rotary maps, and for the skeletons of polyhedral rotary maps (see here for the explanation of the column labels):

• Excel spreadsheet of skeletons of all rotary maps with at least 2 and at most 3000 edges.
• Excel spreadsheet of skeletons of all polyhedral rotary maps with at least 2 and at most 3000 edges.

The skeleton graphs can be explicitly contructed within the magma package available for download in a zipped file (141 MB). The functionalities of the magma package are described in the description file for the census by the number of edges.