Henry Segerman
Henry Segerman is an associate professor in the department of
mathematics at Oklahoma State University. His research interests are
in three-dimensional geometry and topology, and in mathematical art
and visualization. In visualization he works in 3D printing, spherical
video, virtual, and augmented reality. He is the author of the book
"Visualizing Mathematics with 3D Printing".
This variant of the classic 15 puzzle differs in the addition of
four extra tiles, jammed into the puzzle by replacing the usual
$4\times 4$ frame with five $2\times 2$ squares, hinged around a
central vertex. A tile can slide across the hinge between two
squares when there is no angle between them. The puzzle has a cone
point with angle $5\pi/2$ in the center. A consequence of this
point of negative curvature is that the puzzle has non-trivial
holonomy: a tile that travels around the central point comes back
rotated by a quarter turn. Thus the orientation of the tiles is
important.