2020 Joint Mathematics Meetings
Edward Vogel
Artists
Statement
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.
Artworks
About Fifty
38 x 48 cm
Computer Graphics
2019
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