“Vergence” by Tina Frank

An “oloid” via Wundersames Sammelsurium

“Shortest Path on the Surface of Convex Polyhedron” by Joseph O’Rourke at Smith College.

“Convex Hull Of 1000 Random Points on a Sphere” by Jon McCammond of the Mathematics Department at UCSB.

The modern mathematician finds the space of three dimensions, in which our visible universe is containled, entirely too contracted for his conceptions, and is obliged to imagine a space of “n” dimensions in order that his fancy may find room to disport itself. But it is a new idea, on the part of the novelist, to make the conceptions of transcendental geometry the basis for an amusing story.

The very short article goes on to compare “Flatland” with “Through the Looking Glass” and their use of geometry as speculative and imaginative.

In trying to find more about this term, it appears that sadly the intelligent design crowd has laid claim to it.  The most I could find (in an admittedly short search) was this related Wikipedia article on “Complex Geometry“:

In mathematics, complex geometry is the study of complex manifolds and functions of many complex variables. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric chapters of complex analysis.

Sometimes I think I should start a separate blog of just shapes.  This beauty is called a “Great Dirhombicosidodecahedron“, and it is great.  Perhaps there is a dissertation somewhere on why we are drawn to certain shapes like this one and not others (for example, I have no love for the “Great icosidodecahedron“).

Image via: Wikipedia’s “List of Uniform Polyhedra”

Via: Investigating Patterns: Polyhedral Patterns