It's created easily but it has some weird properties. Take a cone and rotate it around its base so that the top traces out a circle in zw. The resulting object is build similar to a duocylinder, but with dicones as sections instead of cylinders. One can also see it as a disk that is tapered while extending radially outward in zw to form another circle as its edge. The resulting shape consists of only one face coiling around two 90°-edges in the shape of orthogonal circles. It has two rotational symmetries - one in the xy-plane, one in the zw-plane.

It's rolling behaviour is for sure the most complex among simple 4D objects. It would be an intersting object just to push and watch moving.

- When its lying on its face, one point of each edge is touching the ground.

- It can roll in two directions (and linear combinations of them). When it's rolling in one of them, the point one edge touches the ground stays the same while the other edge roles like an inclined wheel, tracing out a circle.

- Even though it has only two degrees of motion it can trace out the whole 3-plane. This is a feature of the trajectories in the two main directions being curved - if it rolls around one circle, the plane of the other circle is rotated - it traces out a circle on a circle on a circle and so on.

- I have no idea what a movement off the main rolling directions looks like. The trajectories might look chaotic or form nice open or closed patterns. Would be interesting to simulate them with the computer (anyone interested? ).

- Moving by a distance smaller than the object itself in the third direction (where it can't go directly) is not an easy task.