# Edward Vogel

I use art to reveal the mathematics of tiling and packing puzzles such as polyominoes and the SOMA Cube. The solutions to these puzzles lend themselves well to interesting discoveries by combinatorics, symmetry and its representation as graphs. In addition to representation I build interactive exhibits utilizing enlarged scale and quantities of puzzles pieces.

My father asked me how long it would take me to solve the SOMA
Cube puzzle. Finding a single cube solution took me less than a
minute. How many solutions and how to represent them took "about
fifty" years.

1. Background - spreadsheet of all 240 solutions sorted on the
"Purple Crystal" to uncover structure

2. Midground - tree graph of all 240 solutions

3. Foreground -

a. branch detail of twelve similar solutions. 3x3 arrays of three
concentric circles

represent the twentyseven cubelets of the cube solutions. The
largest circle is a top layer cubelet, mid circle

a mid layer, smallest circle bottom.

b. SOMA Cube pieces on the left. Solved Cube and SOOs(Symmetry
Operation Objects) on the right.

Four unique SOMA Cube solutions assembled together in larger cube which is cleaved to reveal an example of a Klein Four Group