June 1st, 2009, 03:42 AM  #1 
Newbie Joined: Jun 2009 Posts: 2 Thanks: 0  What shape is this?
There are many video games where the screen "wraps around"  that is, if you go off the top, you end up at the bottom (and vice versa), and if you go off the left you end up on the right (and vice versa). The arcade classic Asteroids is one example. It occurred to me a while back that the playing area in these games is not a sphere, but rather a torus. Now imagine instead a video game that takes place in a cube, where in addition to the left/right, top/bottom rules above, you can also run out the back and end up in the front, and vice versa. My question is, topologically, what shape does this represent? 
June 24th, 2009, 03:24 AM  #2 
Member Joined: Aug 2007 Posts: 42 Thanks: 4  Re: What shape is this?
Circle times the torus?

June 25th, 2009, 10:56 PM  #3 
Newbie Joined: Jun 2009 Posts: 5 Thanks: 0  Re: What shape is this?
I believe it would just be a nextdimensional torus. Interestingly, here is the idea and application of what you're suggesting. http://www.traipse.com/stereoscopic_display/index.html 
June 27th, 2009, 06:36 AM  #4 
Member Joined: Dec 2007 Posts: 43 Thanks: 0  Re: What shape is this?
The shape you described is a oneholed torus.

June 27th, 2009, 07:39 AM  #5  
Senior Member Joined: Jun 2009 Posts: 150 Thanks: 0  Re: What shape is this? Quote:
 

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