The definition of a triangle center is satisfied by infinitely many objects.

Structure Synth is an application for creating 3D structures from a set of user specified rules. It is an attempt to make a 3D version of Context Free.
It is built in C++, OpenGL, and Qt 4.3. Builds are currently provided for Windows and Mac. It is possible to compile Structure Synth on Linux as well.
As of now this project is usable, but it is still beta quality (although it is quite stable, not all planned features are completed). The progress and design considerations can be tracked at the Syntopia blog.

There are remarkably few constructions of aperiodic sets of tiles known, even forty years after Berger's groundbreaking construction.... The undecidability of the Domino Problem ensures that there must be infinitely many distinct principles of construction, and that in fact, there exist aperiodic sets of tiles for which there can be no proof of their aperiodicity!

Paper giving overview of the properties of the gomoboc. The math isn't too hard, the first & last pages are most interesting to the non-mathematician

In 2D; the polygon of points closer to x than any other point. "John Snow used a Voronoi diagram in [uberfamous] 1854 [map] to illustrate how ... the Soho cholera epidemic [clusted around] the infected Broad Street pump"

"The Biblically possible shapes of the Earth"

drilling square holes

fun & addictive little game. must go back to work!

the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the Archimedean solids, and the two infinite families of prisms & antiprisms). There exist exactly 92 Johnson solids.