[ Axial and sliding symmetries (other).] [ Examples and counterexamples. Constructions ]

Author: Yashchenko I.v.

On a sheet of graph paper, several cells were colored in such a way that the resulting figure had no axes of symmetry. Vanya colored one more cell. Could the resulting figure have four axes of symmetry?
To construct an example, one needs to take a figure with four axes of symmetry and remove a cell that does not lie on any of these axes. For example, a square has four axes of symmetry (see the left image). This results in the example in the center.

There are other examples (for example, on the right image).
![](https://cdn.mathpix.com/cropped/2024_05_06_7181633d50815d79481eg-16.jpg?height=452&width=1288&top_left_y=1766&top_left_x=387)

## Answer

It could.