To the lecture series English top page
Comments on Lecture 11 "Card Marks Floating on a Mirror"
Comment 1. Conditions for a figure to be realized as a reflexively-fused object
The figure should satisfy the following conditions.
(1) The figure can be decomposed by a horizontal line into two connected components.
(2) The boundaries of the upside-down version of the lower component and the upper component should have a one-to-one correspondence such that the coresponding points are vertically aligned in the same order.
In the left example, if we start at the leftmost points and travel the boundaries clockwise, we can keep the vertically aligned pair of points between the upper and lower elements.
Comment 2. Reference on the reflexively-fused objects
K. Sugihara and M. Moriguchi: Reflexively-Fused Cylinders. Symmetry, vol. 10, no. 7 (2018), p. 275.