Unsolved geometry problems

[Einstein's Cat]

What unsolved geometry problems are there?

 

[micromass]

https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics

 

[ProfuselyQuarky]

You know, when you read one of those conjectures, you think, "hey, why is this so hard to prove". After taking out your pencil and paper you then realize why. My favorite is the Collatz conjecture. Hail the almighty 1.