Data for the n X n SC(n,n) grid (that is, for the n X n array of squares). 
The counts of regions, edges, vertices are A255011, A331448, A331449.
The total numbers of interior vertices are in A334690.
The numbers of interior vertices counted by degree are in A334691.
The numbers of cells counted by number of sides are in A334699.

SC(n,n): the complete data on valencies and cells
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Making rectangle with dimensions: 2 by 2 ...
Total cutting lines = 16
cutting with line: 1 out of 16
Total polygons = 56
Extra edge points = 0
Different edge numbers = 2
3-gons ::: 48
4-gons ::: 8
Total edges: 92
Total vertexes: 37
Vertex line count stats:
                2 -> 20
                3 -> 8
                4 -> 1
 
 
 
=================================================
 
Making rectangle with dimensions: 3 by 3 ...
Total cutting lines = 42
Total polygons = 340
Extra edge points = 0
Different edge numbers = 3
3-gons ::: 204
4-gons ::: 112
5-gons ::: 24
Total edges: 596
Total vertexes: 257
Vertex line count stats:
                2 -> 204
                3 -> 32
                4 -> 8
                6 -> 1
 
 
 
=================================================
 
Making rectangle with dimensions: 4 by 4 ...
Total cutting lines = 80
Total polygons = 1120
Extra edge points = 0
Different edge numbers = 3
3-gons ::: 680
4-gons ::: 384
5-gons ::: 56
Total edges: 1936
Total vertexes: 817
Vertex line count stats:
                2 -> 616
                3 -> 152
                4 -> 20
                5 -> 8
                6 -> 4
                8 -> 1
 
 
 
=================================================
 
Making rectangle with dimensions: 5 by 5 ...
Total cutting lines = 130
Total polygons = 3264
Extra edge points = 0
Different edge numbers = 5
3-gons ::: 1660
4-gons ::: 1072
5-gons ::: 448
6-gons ::: 76
7-gons ::: 8
Total edges: 6020
Total vertexes: 2757
Vertex line count stats:
                2 -> 2428
                3 -> 252
                4 -> 36
                5 -> 16
                6 -> 4
                10 -> 1
 
 
 
=================================================
 
Making rectangle with dimensions: 6 by 6 ...
Total cutting lines = 192
Total polygons = 6264
Extra edge points = 0
Different edge numbers = 4
3-gons ::: 3416
4-gons ::: 2392
5-gons ::: 400
6-gons ::: 56
Total edges: 11088
Total vertexes: 4825
Vertex line count stats:
                2 -> 3968
                3 -> 572
                4 -> 156
                5 -> 72
                6 -> 16
                7 -> 8
                8 -> 4
                10 -> 4
                12 -> 1
 
 
 
=================================================
 
Making rectangle with dimensions: 7 by 7 ...
Total cutting lines = 266
Total polygons = 13968
Extra edge points = 0
Different edge numbers = 5
3-gons ::: 6348
4-gons ::: 5236
5-gons ::: 1840
6-gons ::: 504
7-gons ::: 40
Total edges: 26260
Total vertexes: 12293
Vertex line count stats:
                2 -> 11164
                3 -> 900
                4 -> 120
                5 -> 52
                6 -> 16
                7 -> 8
                8 -> 4
                14 -> 1
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