# Henry Segerman

Associate Professor of Mathematics

Oklahoma State University

Stillwater, Oklahoma, USA

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".

15 + 4 puzzle

5 x 9 x 9 cm

3D printed nylon plastic, dye, acrylic paint

2021

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.