No. When it comes to 4 dimensions, rotating gets complicated. There's a few types types.. OPs picture is a simple rotation.

Think about it this way.....

ROTATIONS IN 3D

In 3D, think about the X, Y, and Z planes. Here is a pic explaining them. There are 3 different ways it can rotate.

• Here is a rectangle rotating on the XZ plane.
• Here is a rectangle rotating on the YZ plane.
• Here is a rectangle rotating on the XY plane.

The thing is... the XY rotation looks 2D because it uses only the 2 axes that make up 2D (X and Y).

Does this make sense?

ROTATIONS IN 4D

The exact same applies to 4D. Because we can only see in 3D, we can't see this extra dimension (abstract as it is), so all the rotations that use only the X, Y and Z axis look the same as the 3D version. This counts for 3 out of the 6 possible rotations (XY, XZ, and YZ).

The other 3 rotations use the 4th dimension which is marked as W. The rotations along the W planes are XW, YW, and ZW. They look like they are turning inside-out because there is no way to show 4D on a 3D animation. It's not actually turning inside out... This is merely an artifact of projecting from 4D to 3D. The cube is staying the same shape throughout the whole thing.

TL;DR: Our eyes can't see in 4D so we have to imagine a 4th dimension. OPs picture is rotating (not stretching) because it's staying the same shape throughout the cycle.