LƦ | Ʀamblings

Boundary Objects

I've always been fascinated by the fact that we cannot fully perceive (with vision) a 3D object. For example, a cube just appears to be a cube, there is no guarantee that the parts we cannot see actually conform to the geometry of a cube (8 vertices, 12 edges and 6 faces).

It could be - for example - a "Q-sphere" (where Q stands for cube). One side looks like a cube but a rotation of 180 degrees reveals that one face of the cube is replaced by an hemisphere. Also, a cube could be hiding other shapes, like a pyramid.

These are just simple examples, but what if we start to introduce holes, or multiple dimensions (higher than 3)? What representation can be found for these mesmerizing objects?

Using graphs and steering away from Euclidean geometry, it is possible to come up with a representation that captures the details of these elusive objects.