# Icosahedral Order in Materials Science and Geometry

Part II: If not tilings, then what?

## Marjorie Senechal, Smith College

## December 8, 2015

Scientific revolutions occur in not one but two phases: first, the
demise of a paradigm (see Thomas Kuhn's *The Structure of Scientific
Revolutions*) and second, removing unexamined assumptions that had
propped it up. The Copernican revolution abolished geocentricity but
not circularity: it remained incomplete until Kepler. The lesser but
instructive revolution in the materials sciences sparked by the
discovery of aperiodic crystals follows that pattern: periodicity is
gone, and we are clearing out its props. My talk will consider three
challenges in modeling aperiodic crystals:

- Why not tilings?
- The local-global dialogue.
- New problems in discrete geometry.

The foundations are in my 2013 Mathematical Intelligencer article with
Jean Taylor, who gave the independent-but-coordinated Part I on real
materials in this seminar on November 10.