Kokichi Sugihara's Homepage (Japanese)

Comments on Lecture 12 "Paper-Made Ambiguous Cylinders"

Comment 1. Conditions for a figure to face opposite in a mirror

An ambiguous cylinder having a rectangular section that turns opposite in a mirror can be constructed if the goal figure satisfies the next two conditions.
(1) It is symmetric with respect to a horizontal line.
(2) The upper boundary curve, as well as the lower boundary curve, is point-symmetric with respect to the middle point.
For the left example, the figure is symmetric with respect to the broken line, and the upper and lower boundary curves are point-symmetric with respect to the middle points. Thus, it satisfies (1) and (2).

Comment 2. Diagrams of the unfolded surfaces of paper objects

The following objects can be constructed from the unfolded surfaces printed on a hard sheet of paper. Make a rectangular cylinder so that the printed side faces inward.

Space fighter and star

Here is the diagram.

Arrow that faces opposite in a mirror

Here is the diagram.

Bottle and wine glass (horizontally placed cylinder)

Here is the diagram.