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[Preprint]. 2023 Dec 25:2023.05.30.542747. Originally published 2023 May 30. [Version 2] doi: 10.1101/2023.05.30.542747

Table 2.

List of possible grid maps and properties of these grid maps given the total number of neurons participating in a trajectory-coding sequence in a rectangular environment. For each grid map that has a non-zero angle to a border, a reflection or 90°-rotation and reflection up to relabeling of the cells exist, and these additional possibilies are not included in this list.

# neurons Repeat lengthsa Lattice type Smallest angle to a border of a rectangular environmentb
7 7, 7, 7 Hexagonal 10.9°
8 4, 8, 8 Centered rectangular
4, 8, 8 Oblique 10.9°
9 3, 3, 3 Hexagonal
3, 9, 9 Oblique 10.9°
3, 9, 9 Oblique 13.9°
3, 9, 9 Oblique 16.1°
10 5, 10, 10 Oblique
5, 10, 10 Oblique 10.9°
5, 10, 10 Oblique 16.1°
11 11, 11, 11 Oblique 6.6°
11, 11, 11 Oblique 10.9°
11, 11, 11 Oblique 16.1°
12 6, 6, 6 Hexagonal
3, 12, 12 Rectangular
3, 12, 12 Rectangular 10.9°
3, 4, 12 Oblique
3, 4, 12 Oblique 13.9°
4, 6, 12 Oblique
4, 6, 12 Oblique 6.6°
4, 6, 12 Oblique 23.4°
a

Repeat lengths across the three major axes of the hexagonal lattice structure of densely packed firing fields.

b

The smallest angle to a border of a rectangular environment assumes that one sequence of cells is arranged in parallel to one wall.