Let them be

In the previous post on curvahedra spheres, we actually missed an interesting collection of curvahedra balls, as we assumed that every face had at least 3 sides. This makes a lot of sense as for polygons with straight edges you have to have three sides.

For curvahedra, however, with their curvature, you can have two different paths of shortest length going between two points. Think about going round either side of a hill.

This gives a two sided polygon, or bigon, and a cute collection of Curvahedra. The bigon balls:

This effect of curvature can be seen in the night sky. Objects with significant gravity, such as galaxies and black holes significantly curve the space around them.  Light, wanting to travel the shortest distance goes passes round the object in many different ways, rather than passing straight through, in a process called called gravitational lensing.

This can be seen as a repeat of the same star several times, for example in a astronomical feature called Einstein’s cross:It can reveal black holes and magnify distant galaxies, and provided an important piece of evidence for general relativity.

You can get your own Curvahedra pieces to explore!.