Dance Squared

A fantastic video showing a multitude of transformations and symmetries of the square. Marvel as the square bisects, reflects and dances to the music. A link for the equally amazing Notes on a Triangle follows.

Notes on a Triangle is a similar geometric ballet to Dance Squared only this time with a triangle. How are such transformations possible with the triangle? What other geometrical shapes would contain such symmetry? Why not try it with different quadrilaterals?