Rotation Symmetries of Antiprisms

An antiprism can be rotated to occupy the same region of space as it did originally. However, this permutes the faces. Beside rotating around the vertical axis, you can rotate around certain lines through the center of mass of the antiprism, depending on the parity of the number of faces.

In this puzzle, the labels of the faces are shown in their original positions in the first row of the table. The second row shows where some of those faces land after the rotation. Your job is to fill in the rest of the second row of the table.

Drag the image to see the hidden faces.