For this task, you will need 2 pieces of paper, 1 pencil, and 1 needle.
Cut a square out of one piece of paper. Take a square and place it on another piece of paper. In any place of the square stick a needle. Draw around the square as a template, so that you have the same shape on your sheet. Now rotate the square randomly and draw around it again. Then repeat the rotation and draw another square in the same way. Do these steps 27 more times. As a result of these actions, there will be 30 identical squares on the sheet. Will the intersection of all these squares be a convex set? Which shape does the intersection of 30 squares look like?
Write down your answer for the questions through space. For example, No triangle or Yes square.
You may attach the resulting drawings in the comments.