## Boundary Objects

2023-06-08 | tags : structure | objects, geometryI'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.