If you have a regular cube in an infinite plane, can you rotate it infinitely with the paths of each individual point never crossing itself? (So Point A's path never crosses itself, Point B's path never crosses itself, etc.)

Question

youngster · Answer

what do you mean by "never crosses itself"?

anonymous · Answer

Imagine Point A has a red marker on it.As the cube is being rotated around itself, that red marker makes a line that moves and follows where Point A goes. That red line cannot intersect with itself. The same goes for the other points as though they too have individual markers on them.

youngster · Answer

It could spin infinitely without it crossing but it can, of course.

anonymous · Answer

Is that so for all the corners of the cube, not just the two I mentioned?

anonymous · Answer

I CANNOT UNDERSTAND UR QUESTION...

anonymous · Answer

What about it can you not understand? I can try to clarify it for you, but not if you have no intention to actually answer me.

anonymous · Answer

iam not an expert...to my imagination well this is possible...only if we rotate once....to rotate infinitely i think we have to change the axis of rotation for every full rot...

youngster · Answer

|dw:1340890856152:dw|Yes--you would have to change the axis of rotation or at least move it along the axis.

anonymous · Answer

u mean like the points tracing a helical motion?

youngster · Answer

yes

anonymous · Answer

if you rotate a cube for some countable times in 3d it is possible that paths of corners do not intercept but if you rotate it for infinite time then it will become an imaginary sphere of paths of corners. then they must be coinciding.

anonymous · Answer

but if you consider 2d with one dimension as a plane to move it upon then yes it is possible. . .