07 Nov

Deltahedral Torus?

Here’s a torus built from equilateral-triangle Geometiles that I used as a prop for an undergraduate talk at Harvard University in the Fall semester of 2018. Actually, the structure it is based on is not mathematically exact; the triangles theoretically are isosceles triangles of sides 1, 1, and 0.998, but there is plenty of give in the real world to construct it physically. As far as I know, it remains an open wuestion whether there is a true deltahedral torus in which all vertices are hexavalent.