5th Generation Impossible Objects (2016-)

"Topology-Disturbing Objects" whose topology changes in the mirror

This class of objects change their topology in the mirror although the shape of each component does not change. "Topology" is the mathematical property representing how figures are connected/disconnected. The topology should not change when an object is reflected in a mirror. The topology-disturbing objects, however, disturb this property. They can be constructed using the same principle as ambiguous cylinders 　 in a slightly different manner.

Topology-Disturbing Object "Vertically Aligned Crossing Circular Cylinders"

If we see the object directly, it consits of two circular cylinder mutually separated from each other, but in the mirror they intersect. This object is made by a 3D printer, but it can also be constructed by paper.

The diagram of unfolded surfaces is posted in the next page:
"Vertically Aligned Circular Cylinder" unfolded surface 1 　
>"Vertically Aligned Circular Cylinder" unfolded surface 2 　

Enjoy various topology-disturbing objects.

This object can be made using paper. The unfolded surface diagram is here. 　

This object can be made using paper. The unfolded surface diagram is in the Japanese book:
杉原厚吉：「錯覚トリックキット」、幻冬舎

Movies of the topology-disturbing objects

Ambiguous Cylinders 4

The theory of the topology-disturbing objects can be found in the nest reference.
K. Sugihara: Topology-disturbing objects: A new class of 3D optical illusion. Journal of Mathematics and the Arts, vol. 12 (2018), issue 1, pp. 2-18. The abstract is here.

To Kokichi Sugihara's English Top Page