Week 3

1. The crystalline structure of "apollohedron".

2. The homomorphism from the Euclidean group to Lorentz group, and their actions on the set of disks and the Minkowski space, respectively  $$\frac{\hbox{Eucl} (2)}{\mathcal D_2}  \quad \longrightarrow\quad \frac{\hbox{SO}(3,1)}{\mathbb M^{1,3}}$$  Just translations for now.

PS.  The above diagram is "approximate".  We shall extend it to the conformal group and take care of some details.  

[Click to enlarge]