Test Your Intuition (34): Tiling high dimensional spaces with two-dimensional tiles.

A tile Image may be NSFW.
Clik here to view. is a finite subset of Image may be NSFW.
Clik here to view.. We can ask if Image may be NSFW.
Clik here to view. can or cannot be partitioned into copies of Image may be NSFW.
Clik here to view.. If  Image may be NSFW.
Clik here to view. can be partitioned into copies of Image may be NSFW.
Clik here to view. we say that Image may be NSFW.
Clik here to view. tiles Image may be NSFW.
Clik here to view..

Here is a simpe example. Let Image may be NSFW.
Clik here to view. consists of 24 points of the 5 by 5 planar grid minus the center point. Image may be NSFW.
Clik here to view. cannot tile Image may be NSFW.
Clik here to view..

Test your intuition: Does Image may be NSFW.
Clik here to view. tiles Image may be NSFW.
Clik here to view. for some Image may be NSFW.
Clik here to view.?

If you prefer you can think about the simpler case of Image may be NSFW.
Clik here to view. consisting of eight points: the 3 by 3 grid minus the center.

Image may be NSFW.
Clik here to view.

I forgot to add polls…