Well, from one perspective, since the requirement is that a tile must be able to tile the plane only irregularly;
- All three-sided shapes can tile the plane regularly,
- All four-sided shapes can tile the plane regularly,
So we know the minimum number of sides is at least five.
Assuming 13 sides is established as the minimum, I suspect there is no 'nice' reason for it; its just that this may be the minimum number to give you sufficient degrees of freedom.
Comments
Well, from one perspective, since the requirement is that a tile must be able to tile the plane only irregularly; - All three-sided shapes can tile the plane regularly, - All four-sided shapes can tile the plane regularly,
So we know the minimum number of sides is at least five.
Assuming 13 sides is established as the minimum, I suspect there is no 'nice' reason for it; its just that this may be the minimum number to give you sufficient degrees of freedom.