An Ancient Tiling Problem

This menacing creature is Glyptotherium texanum.  Well, was Glypotherium texanum.

The armor caught my attention.  It’s made of small plates that create an interesting tiling of a curved surface.

Notice how the tiles slowly change from quadrilaterals to pentagons to hexagons, and back again!  I wonder what factors determine the shape of each tile as they grow.