Abstract: A transformational folding puzzle assembly is formed of 24 identical tetrahedrons hingedly secured in a chain or ring. The tetrahedrons are all-space filling, and may be isosceles or other configurations. This hinged structure provides: 1) the construction of a great variety of new shapes, more than a hundred with diamond faces and hundreds more without that limitation; 2) A variety of shape dependent puzzles including a family of geometric transformational magic shapes; 3) a transformational four year calendar/ball in which the twelve months of the year are expressed on the 12 diamond faces of the ball exteriorly while the other three years are hidden in the interior of the rhombic dodecahedron ball; 4) a mechanism for holding the shapes together and joining them to one another, forming for a construction set in which each chain can transform into hundreds of other possible pieces.