Originally posted by rheymans
If you are looking for the 3D equivalent of the mobius strip, it is called a Klein Bottle. A true Klein bottle is actually 4 dimensional, but we (humans) make 3D projections of true Klein Bottles, and the inside does turn out to be the outside.
Would you care to elaborate on that?
The mobius strip is still 2 dimensional btw...a cilindric shell is also 2 dimensional.
There is a formula so calculate the dimension of an object:
D = log(f)/log(2)
D is the dimension, f is the factor. The factor is how many times the object increases in size when the length/withs/depth/.. are doubled.
A cube thus has factor 8 and has dimension D=log(8)/log(2)=3
A mobius strip becomes 4 times as large and thus has dimension D=log(4)/log(2)=2
The Bottle has dimension 3.