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.
In this sequel to the 15 + 4 puzzle, every vertex has five squares
around it. This makes the puzzle considerably harder to solve.
Even sliding a tile from one square of the frame to a neighbour
can be difficult: the whole frame must be manipulated to get the
two squares to be flat, possibly requiring many preparatory moves.
There are no neat rows to put the numbers in for the solved state:
instead the numbers spiral out from the center, each pointing to
the number following it.