But there are two ways one can "twist" a square prism (or rectangular prism):

• If I physically twist a clay prism, the four connecting squares (or rectangles) become twisted parallelograms ( not the solid shown).
• If I rotate the top square relative to the bottom square, and only allow straight edges and planar faces, nothing "slips" or "snaps" (like with the gyrobicupolae ). I must replace the four connecting squares (or rectangles) with four pairs of triangles (as shown here). That operation seems like more than just "twisting". Also, the resulting " twisted prism is topologically identical to the antiprism " – a prism becomes an antiprism for any twist other than 0 degrees.

If I rotate the top square relative to the bottom square of a uniform [or regular] square antiprism , the triangles change proportions, but the number of faces does not change.