Tiling

...?

Spherical Dodecahedron

a.k.a. pentagonal tiling of the sphere

+ Stereographic Projection

= Stereographic Dodecahedron

Rotation

...of what?

z \mapsto \frac{i (z+1)}{z-1}

The Hyperbolic Plane!

4-D Rotations

Enneper’s Surface

Möbius Band

Geodesic

Acute Triangles

Drum

Catenoid/Helicoid