Equilateral Triangles in 3D with Integer Coordinates

n

1

2

3

4

5

The number of equilateral triangles with integer coordinates in a cube of size

n

depends on the "minimal" equilateral triangles defined in such a cube and all the transformations of such triangles. This Demonstration shows the minimal triangles along with the total number of equilateral triangles for

n

= 1 to 5.