# 4 identical shapes that touch each other?

It is known that one can have 4 shapes in a plane all touching each other, and not 5. You can add requirements to the 4 shape problem:

• Can you do it with 4 equal triangles? (No)
• Can you do it with 4 equal rectangles? (No)
• Can you do it with 4 triangles with equal area? (Yes) (figure 1)
• Can you do it with 4 equal shapes? (Yes) (figure 2).

My question is: what is the simplest single shape which you can do it with?
(Figure 2 was easy to find, but it looks like it can be improved upon ;-).
(Simpler is undefined, but build from less than 11 squares would fit)
(I could not find a source to this problem. Is there?) • Does it count as the same shape if you use its mirror image? Jan 4, 2018 at 16:16
• See 5 geometric shapes, all touching each other for why five is impossible. Jan 4, 2018 at 16:38
• @Tweakimp: figure 2 has mirror images. Avoiding this would be nice (just my feeling), but I did not state that requirement. It is a bonus. Jan 4, 2018 at 16:42
• Does the shape have to be continuous? Jan 4, 2018 at 20:41
• See also this Mathematic SE post or a solution with mirror-symmetric pieces. Mar 3 at 6:24 