Permutahedra

The 1-skeleton of the permutahedron of Type A3.

Cambrian Lattices

Cambrian lattice equivalence of Type A3 with c=123 and c=213

Cambrian lattice of Type A3 with c=123 and c=213

Generalized Associahedra

Polytopal realization of the (simplicial) 3d-associahedron of Lee

Geometric representation of the cyclohedron (or Type B associahedron)

Polytopal realization of the 3d-associahedron of Chapoton-Fomin-Zelevinsky

Polytopal realization of the 3d-associahedron of Hohlweg-Lange-Thomas with c=123

Polytopal realization of the 3d-associahedron of Hohlweg-Lange-Thomas with c=213

Polytopal realization of the Type B 3d-associahedron of Hohlweg-Lange-Thomas with c=123

Polytopal realization of the Type B 3d-associahedron of Hohlweg-Lange-Thomas with c=213

Polytopal realization of the Type H 3d-associahedron of Hohlweg-Lange-Thomas with c=123

Polytopal realization of the Type H 3d-associahedron of Hohlweg-Lange-Thomas with c=213

Polytopal realization of the cluster complexes of type A3 with c=123 and c=213

Common vertices of Permutahedra and generalized associahedra

Singletons of type A2 with c=12 and c=21

Singletons of type A3 with c=123 and c=213

Geometry of infinite root systems

Normalized isotropic cone and the first few thousand normalized roots for the Coxeter graph depicted. The set of accumulation points is dense on the isotropic cone.

Normalized isotropic cone and the first few thousand normalized roots for the universal Coxeter group on 4 generator. The set of accumulation points form an Apollonian gasket.

These pictures are artistic variations with different colors and size for the normalized roots (the closer the root to the isotropic cone, the smaller it is represented).

TikZ + Sage to draw 3D-polytope

I wrote a patch to the Polyhedron module to write a TikZ-image script (see here)

A custom Sagemath logo

A greatrhombicuboctahedron

A pentakis dodecahedron