Modular hyperbolic tilings
 A 12 colors tiling related to the usual subgroup of the modular group, highlighting the 3 cusps
 Another colouring of the same picture; the union of the 2 biggest visible tiles form the standard fundamental domain
 A conformal grid growing from the 'spine'
 Higher resolution
 The image of the coulouring scheme by the (pre)modular function
 Higher resolution

Modular hyperbolic tilings, black and white
 Tesselation by some fundamental domain for the modular group (high resolution)
 Another fundamental domain
 Yet another
 A fundamental domain for an index 2 subgroup
 A fundamental domain for an index 3 subgroup
 A fundamental domain for an index 6 subgroup
 A fundamental domain for a coindex 2 supgroup

Klein's quartic. A very symmetric complex-curve (a.k.a. Riemann surface) in P2C.
 Klein told us: glue this fundamental domain the right way (2 solutions, not so obvious), and you'll get a very symmetric Riemann surface.

Ahlfors and Grunsky's conjectural optimal function for Bloch's constant
Topology
 Surfaces of genus 1, 2 and 3

Measure preserving maps
 Agate?
 Mixing
 Mixing on the sphere
 Hypnose

Polytopes
 Three patterns of the 24-cell
 Three patterns of the 24-cell
 Some patterns
 Écorché de l'ombre du 120

An Archemedean polytope
The Runcinated 120-cell is a polytope. It is Archimedean in the sense that its organization at every vertex is the same, and all its chambers are Archimedean polyhedra too: regular dodecahedra, prisms with regular pentagonal base and square sides, prisms with equilateral triangular base and square sides, and regular tetrahedra. Here, these objects are respectively represented green, purple, yellow and orange. To represent the object, it is projected orthogonally to the three dimensionnal space and then rendered into a 2D image. We used LuxRender for a photorealistic look.
 The outer shell is made of flattened cells and completely encloses the interior. We broke the shell to reveal cells below.
 Same, without the outer shell. The cells are shrunk a little bit, to enhance visibility.
 By accident, some groups of cells are neatly separated by planes.
 Undraping the polytope
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 Showing only tri-prisms
 The dual of the polytope
 A view of the inside

Dodecahedral fundamental domain of the Seifert-Weber hyperbolic space
 The set, sitting in the ball model of hyperbolic space.
 The domain is the intersection of half-spaces bounded by hyperbolic planes
 Looks like a flower

A Kleinian reflection group with a Sierpinski limit set
 The group is generated by the reflections along the 4 blue circles. Black: limit set. Yellow tones: generated tesselation in the discreteness set.
 They are arranged so as to have a tetrahedral symmetry and so that they intersect at angle a turn / 7
 An index 24 subgroup has the following tetrahedral fundamental domain
 A cubemap if you want to play with a visualizing tool
 well... if your tool accepts cube maps
 A spheremap
 ... if you manage to find a visualizing tool

Sphere viewer
In fact, I have written a viewer: test it on the links here and here

 A non geometrically finite end of a finite type Kleinian group
 Fundamental domain for an hyperbolic structure of an Anosov suspension of a punctured torus

Boy's surface
Boy's surface is a non-orientable self-intersecting surface, it is also an immersion of the projective space RP2 into R3