If you are working with topological field theoretic Hopf fibrations, chaotic attractors, and/or E8 and any of its extensive set of maximal subgroups, polytopes, lattices and codes or its folded (rotated) H4 family of polytopes (e.g. 600 and 120 cells in their vertex, cell, face, and edge orientations), VisibLie_E8 can group theoretically integrate all of these concepts visually!
Click on the PNG image to get the SVG version.
This is all also related to the Clifford algebra of Cl(9,0) with the Bott Periodicity clock showing the related algebras (click for SVG):
The Bott periodicity clock uses a Mod 8 clock face with second hand mnemonics taken from the I-Ching with the real Clifford algebra of signature (p,q) denoted as Clp,q(R)=Cl(p,q). An animated (GIF) example is on the Bott Periodicity Wikipedia page.
A few more geometries:
