Simple k-Angulations
Simple k-Angulations is the family of simple 2-connected plane graphs such that all faces (including the outer face) have size equal to the k. This page contains the exhaustive list of k-angulations for k=3,4,5,6,7,8,9,10 of small orders.

The graphs are in planar code format. A complete definition can be found in the plantri manual (Appendix A). For the graphs on this page, the following should be adequate. Each graph is given as a sequence of bytes, starting with a byte containing the number of vertices. Then for each vertex, a list of the neighbours is given, one neighbour per byte in clockwise order, plus a zero byte to end the list. Vertices are numbered starting with 1. A graph with n vertices and e edges thus occupies exactly 1+2e+n bytes.

I would be very happy to know the problem you are working which needed this data set. So if you could give me your name and email, I will be very happy to discuss it with you.

Reference:
[1] M. Jooyandeh, Recursive Algorithms for Generation of Planar Graphs, PhD Thesis, College of Engineering and Computer Science, Australian National University, 2014.
[2] G. Brinkmann and B.D. McKay, Fast generation of planar graphs, MATCH Commun. Math. Comput. Chem, 58(2) (2007) 323-357.
[3] G. Brinkmann and B.D. McKay, plantri (software).
[4] R. Bowen, S. Fisk, Generation of triangulations of the sphere, Math. Comput., 21 (1967) 250–252.
[5] V. Batagelj, An improved inductive definition of two restricted classes of triangulations of the plane, Combinatorics and Graph Theory, 25 (1989) 11–18.
[6] G. Brinkmann, S. Greenberg, C. Greenhill, B.D. McKay, R. Thomas and P. Wollan, Generation of simple quadrangulations of the sphere, Discrete Mathematics, 305 (2005) 33-54.
Examples
3-Angulations 4-Angulations 5-Angulations
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3-Angulations (Triangulations)
Count File
Vertex Face Graph
3211KB
4411KB
5611KB
6821KB
71051KB
812141KB
914503KB
101623314KB
11181,24981KB
12207,595542KB
132249,5663.78MB
1424339,7223.82MB
15262,406,84127.9MB
162817,490,241208MB
1730129,664,7531.54GB
1832977,526,957
4-Angulations (Quadrangulations)
Count File
Vertex Face Graph
42Comming Soon
53Comming Soon
64Comming Soon
75Comming Soon
86Comming Soon
97Comming Soon
108Comming Soon
119Comming Soon
1210Comming Soon
1311Comming Soon
1412Comming Soon
1513Comming Soon
1614Comming Soon
1715Comming Soon
1816Comming Soon
1917Comming Soon
2018Comming Soon
5-Angulations (Pentangulations)
Count File
Vertex Face Graph
52133B
843177B
116302.65KB
148855104KB
171047,6987.24MB
20123,324,90763.2MB
2314269,714,526
6-Angulations (Hexangulations)
Count File
Vertex Face Graph
62139B
83155B
1045370B
125121.1KB
1468910KB
16760080.3KB
1886,139949KB
20966,48111.4MB
2210792,68015MB
24129,813,724
7-Angulations (Heptangulations)
Count File
Vertex Face Graph
72145
1246544B
17622127.9KB
22837,0335.91MB
8-Angulations (Octangulations)
Count File
Vertex Face Graph
82151B
113178B
1448856B
175344.12KB
20649173.3KB
2377,3271.22MB
268146,63127.9MB
9-Angulations (Nonangulations)
Count File
Vertex Face Graph
92157B
164101.2KB
236977160KB
10-Angulations (Decangulations)
Count File
Vertex Face Graph
102166B
1431103B
184121.63KB
2257511.7KB
2661,832341KB
30748,3089.96MB