Our teacher gave us a figure, and challenged us to dissect into exactly 4 shapes, that were congruent, in as many ways as possible. I won't reveal details of the specific shape. I am wondering if symmetry can help.
Obviously, allows us to transform dissections and such to get more (except that all my dissections so far share the same symmetry as the shape.) I was wondering if using the symmetry of the shape can help me find new symmetries. (I am hoping I will find a dissection that I can mutate, and then get infinite dissections.)
I don't know much group theory, but I probably know enough to, say, find the symmetry group, find subgroups, find quotients and products and such.
How can I dissect a figure based on its symmetry?