Does Contraction at High Speeds Happen in Any Dimension Besides Length? I'm not sure if this is a duplicate.
Whenever physics buffs talk about Einstein's relativity (I forget which kind) at high speeds, they always talk about "length contraction", or shortening of the object due to the high speeds. This happens even at the relatively low speeds we travel at every day, but there is so little contraction we don't notice it. However, these physics buffs only talk about length contraction, implying a single dimension. Why do they never talk about contraction in more than 1 dimension? Is it because the contraction happens in the direction the object is going, which is usually only a single direction? If so, are there any cases which would involve 2- or 3-dimensional contraction?
 A: 
Is it because the contraction happens in the direction the object is going, which is usually only a single direction?

Yes, exactly. The dimensions perpendicular to the relative motion of the object and the observer are not affected. And as far as I know, there is no motion in which more than one (spatial) dimension is contracted.
A: A simple argument shows that contraction can only occur in the direction of motion: there is no way to uniquely specify any other axis in space along which an object could contract. If nature is to be consistent, then longitudinal contraction is the only choice.
A: " Is it because the contraction happens in the direction the object is going, which is usually only a single direction? If so, are there any cases which would involve 2- or 3-dimensional contraction?"
Yes. In order to illustrate the principle, uniform motion (constant velocity) is usually specified as occurring along a single spatial dimension, such as "the x-axis", with an equation of motion x = vt. Relativistic contraction occurs along the direction of motion, so in this case occurs in one dimension.
If, let's say, motion occurred along a 45 degree path (equation y = x = vt), then you would observe contraction in both the x and y directions. And a generalization to a diagonal in 3 dimensions will produce contraction in 3 dimensions.
It's just a matter of representation.
