From the tetrahedron to the superstring

Geometry lecture for non-geometers.
Speaker: Yasha Neiman.
Title: "From the tetrahedron to the superstring".

In this talk, we'll go on a romp from 3 to 4 to 8 to 10 dimensions, to see how a sequence of fun and geometrically meaningful steps leads from the simplest shape in our familiar 3d space to the vibrations of the superstring in 10d spacetime.
Major roles will be played by 4d numbers called the quaternions, and by a beautiful 4d shape called the 24-cell. 
I will bring some 3d shapes made of Zometool, to visualize as much of this as we can.