The same trick, rolling instead of crawling. A box has three poses: sitting flat, tilted 30° up onto its bottom-right corner, and tilted 60°. Past 60° it lands flat again, one box-width along.

But it lands on its side: the corner it pivoted on is now bottom-left, and the next roll has to pivot on the corner that was top-right. So the edge from 60° back to flat carries "one box-width right, and rename the corners". Renaming points is a linear map on the drawing like any other, so an edge can carry it, and walking the edge backwards renames them back.

Push the box to the right by a top corner. The bottom-right corner is the pivot, so it can't push this roll; after the roll, a different corner is the pivot. Push it left and it rolls back.

Look closely mid-roll: the box shrinks a little. Each pose is placed once when the state enters a zone, and then the placed poses are blended linearly, so a corner cuts across the chord of its arc instead of following it. That's Tom's linearized configuration map. It costs a little accuracy and keeps the drag a small linear solve. More poses make the chords shorter.