The plot concerns Alice, a young woman who drops out of college and starts a company based on the clever molecular modeling techniques that she's invented. Since she's really good with math, the algorithms she uses are really cutting edge and quite clever (incorporating everything, including relativistic and quantum effects). Unfortunately for her, the ideas turn out to have been a bit too clever. They produce some sort of bridge between our universe and another, and some nasty little biting creatures get into her office.

There are various aspects of geometry in the story. I quite explicitly discuss the Platonic solids and the role of the Euler characteristic in categorizing them, non-Euclidean geometry (which is at least implied by the existence of "the object" itself and also the unusual metric properties that allow the "things" to grow in size as they move further from it), and also instantons, which are special shapes that 4-dimensional space can take (which interestingly are impossible in any other dimension).

The story also briefly touches on the notion of a "soliton". From one point of view, an instanton is a special kind of soliton, and so this ties in with the previously mentioned geometry. But, there is more to it than just that. Although most people think of a soliton in terms of waves (like a tsunami), the so-called "topological soliton" is sometimes described as interpolating between two "vacua"...a sudden connection between two different sorts of "emptiness". (See, for example, the article at this location.) It was this notion that brought me to the idea that a soliton in reality could be a physical bridge to another universe. Also important to the story is the fact that such topological solitons always have an "anti-particle", which takes the form of a bridge going in the other direction.

This story is one of the ones which appears in my collection Reality Conditions, published by the MAA.