The cube angles are right angles. But the diagonal supports going from one corner of the outer cube to the corresponding corner of the inner cube are not. My remark is about the angles on the supports.
The inner cube, based on the drawing, cannot be the same size as the outer. The inner’s 6 walls are presented as being inside the outer cube’s walls. For perspective to be in play, at least one wall would have to be outside the outer cube.
That’s only one way (and the easiest) to represent a hypercube.
Another way is to envision two 3d cubes, “open” the corner of one and place it “inside” the other, and connect all the corresponding corners. The resulting 8 cubes, as is in the prior illustration, have 2 that look “normal” and 6 that are skewed due to the down-dimensioning representation in 3d.
Read “And he built a crooked house” by Heinlein for more detail.