Imagine a solid 3-D cube. Now imagine that this cube is traveling close to the speed of light. To what degree will the spatial geometric properties of this object (or in general of any 3-D object) change (as predicted by the Lorentz transformations)?

I assume that despite the changes to shape, some fundamental geometric features of 3-D objects are preserved no matter the frame of reference. I assume that a cube will preserve some of its fundamental geometry Namely, a cube undergoing Lorentz contraction will not become a torus or vice-versa. (I might be wrong about this) But what is the formal limit to these changes? Will the affine structure of a 3-D object undergoing Lorentz contractions change or would its topology also change?

Thank you.

Imagine a solid 3D cube. Now imagine that this cube is traveling close to the speed of light. To what degree will the spatial geometric properties of this object (or in general of any 3D object) change (as predicted by the Lorentz transformations)?

I assume that despite the changes to shape, some fundamental geometric features of 3D objects are preserved no matter the frame of reference. I assume that a cube will preserve some of its fundamental geometry Namely, a cube undergoing Lorentz contraction will not become a torus or vice-versa. (I might be wrong about this) But what is the formal limit to these changes? Will the affine structure of a 3D object undergoing Lorentz contractions change or would its topology also change?