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Max brought me this strange cube for Christmas.
The top and bottom faces are formed of two types of shape, an isosceles triangle with a central angle of 30 degrees and a kite with an angle of 60. The angles on each face must add to 360 degrees. The puzzle starts out with 4 kites and 4 triangles on both faces.
The only transformation that can be performed swaps half the top face with half the bottom face by lining up a diameter on each face with the split on the middle row. The possible faces and the ways they can be split are shown on the unique faces page.
After a few operations the faces are unlikely to remain square.
This page allows you to explore the transformations interactively, more detail about the possible shapes and moves is shown in the associated pages, see the contents.
(c) John Whitehouse 2017