OFFSET
0,3
COMMENTS
The only regular polygons that can appear are equilateral triangles, squares, and regular hexagons.
LINKS
Peter Kagey, Table of n, a(n) for n = 0..100
Code Golf Stack Exchange, Polygons in a cube
Burkard Polster, What does this prove? Some of the most gorgeous visual "shrink" proofs ever invented, Mathologer video (2020).
EXAMPLE
For the 3 X 3 X 3 grid, the a(3) = 138 regular polygons are A102698(3-1) = 80 triangles, A334881(3) = 54 squares, and A338322(3) = 4 hexagons.
An example of each shape, listed by the coordinates of their vertices:
Triangle: (1,2,1), (2,1,3), (3,3,2)
Square: (1,1,1), (2,1,1), (2,2,1), (1,2,1)
Hexagon: (1,1,2), (1,2,3), (2,1,1), (2,3,3), (3,2,1), (3,3,2)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Oct 22 2020
STATUS
approved