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Half of the 12 hydrogens are in axial position, which means their C-H bonds are parallel and appear to stick up and down from the structure, the other half are in equatorial positions; meaning that they are splayed out.
The axial hydrogens can simultaneously swap places with the equatorial hydrogens. This phenomenon is known as ring flipping.
Due to the inherent need of the sp3 single bonds on carbons to reach 109.5 degrees cyclohexane is not a "flat" 3-D form. chair and boat cyclohexanes exist with chair being the most stable, virtually strain free. (111 degrees IIRC)
Cis/Trans isomers of Cyclohexane.
For example, if there is a methyl group on carbon 1 in an axial position, it will interact with the axial hydrogens on carbon 3 and carbon 5.
Note: Somebody with more ambition than myself really ought to post some pics of this stuff. A picture is worth a 1000 words eh? :)