Final answer:
Rotating a shape 360° around any point or its center will always carry the shape onto itself, and for shapes like a cube, 90° or 180° rotations around certain axes will also achieve this. So, the correct answer is d. Rotating the shape 360° around any point or its center.
Step-by-step explanation:
The question pertains to geometric transformations that can carry a shape onto itself, meaning after the transformation, the shape looks identical to its original position.
For any given shape, certain rotations will result in the shape matching exactly with its original orientation. Specifically, rotating the shape 360° around any point or its center will always bring the shape back onto itself as it completes a full circle.
Additionally, some shapes such as a square or cube can be rotated 90° (or a multiple thereof) around their center or certain axes to carry them onto themselves due to their symmetry.
However, the ability to rotate a shape onto itself by 45° or 180° depends on the specific symmetries that the shape has. If we're considering a cube, as described in the initial information provided, a cube can indeed be rotated 90° or 180° around certain axes - the C4 and C3 axes, respectively - to carry it onto itself.
Thus, the correct answer is d. Rotating the shape 360° around any point or its center.