Just like a normal torus is a circle squared, and a cylinder is a circle multiplied by a line, I think of your torus as a circle raised to the 3rd power, with the 3-d surface being embedded in 6 dimensions (three orthogonal sets of two dimensions, each defining a plane that gives a circle as the cross-section). On Wed, Dec 1, 2010 at 13:16, Michael Beeler <mikebeeler@verizon.net> wrote:
What's the proper name for the following "4 dimensional donut"?
Identifying opposite edges of a sheet of paper makes a torus, actually just the surface, either 0 or "1 cell" thick. Identifying 2 pairs of opposite sides of a 3-D rectangular solid (brick) makes a torus skin with some thickness, like the glaze of a donut. Now also identify the third pair of sides of the brick. This connects the inner surface of the glaze to the outer surface. That seems to require a fourth dimension, so I call this a "4 dimensional donut". But what is its correct name?
I'm still working on domino-nets. The smallest "4-D donut" that might have solutions is 4x5x5, for donimos with 1 to 25 pips (no double dominos). This is probably too large for me to either find a solution or to prove there are none, unfortunately.
Thanks, -- Mike Beeler
-- Robert Munafo -- mrob.com Follow me at: mrob27.wordpress.com - twitter.com/mrob_27 - youtube.com/user/mrob143 - rilybot.blogspot.com