Regular Polygon Spiral
It is an interesting mathematical recreation that you can see on the picture, joining polygons at their different edges. The joining edges form a spiral-like form.
You could spend more time on this e.g. by trying to know what will be the position of the center (triangle) in relation to the whole, as it grows... Or you could try to compute some angles, will there be more parallel segments... Or you could try to visualize how this spiral would look like from a greater distance, if continued... Or you could assemble more spirals (each starting from one side of the triangle), how it will look like... So there are many opportunities of mathematical recreation.