# {6,3,3} Honeycomb in Upper Half Space

A 3-dimensional honeycomb is a way of filling 3d space with polyhedra. It’s the 3-dimensional analogue of a tiiling of the plane. However, not only can we have honeycombs in Euclidean space, we can also have them in hyperbolic space. The {6,3,3} honeycomb lives in hyperbolic space.

# Algebraic Numbers

This is a picture of the algebraic numbers in the complex plane, made by David Moore based on earlier work by Stephen J. Brooks. Algebraic numbers are roots of polynomials with integer coefficients. In this picture the color indicates the degree of the polynomial.

# Tübingen Tiling

A systematic way to generate quasiperiodic tilings of the plane is to take a lattice in higher dimensions and slice it at a funny angle. Greg Egan has created an applet that generates quasiperiodic tilings by projecting selected triangles from an $n$-dimensional lattice called the $\mathrm{A}_n$ lattice onto a plane. This particular picture comes from the $\mathrm{A}_4$ lattice.