it's possible to make a regular tetrahedron with integer coordinates that all lie on the vertices of a cube.In
Does this phenomenon occur in any other dimensional space?
Or specifically, for how many is it possible to construct a regular -dimensional simplex with integer co-ordinates that lie on an -dimensional hypercube in ?
Details and Assumptions:
A regular -dimensional simplex in has vertices that are all an equal distance apart. (It's like an -dimensional version of an equilateral triangle!)
Here is the Wikipedia article on hypercubes. (It's like an -dimensional version of a square!)
Note that the analogous phenomena is not possible in dimensions. That is, we cannot create an equilateral triangle with integer co-ordinates that all lie on a square. Check out why, here.