Weird Races and Strange Places

[Bohandas]

Flat Cone/Angular deficit

This is a series of three square rooms wherein if somebody goes into the room, turns 90° right and goes into the next room and then repeats this process they will return to the first room after traveling to two other rooms, rather than the three which would be expected (such that they return to their place of origin after going around only 270 degrees).

I'll draw a map to make things clearer. Each number represents a specific door:

------     
|    |     
|    3     
|    |     
--2----3---
|    |    |
|    1    |
|    |    |
-----------

EDIT:

on a similar note

Angular excess/saddle point

In this set of rooms the party must go around 450 degrees to return to their point of origin

------     
|    |     
|    3     
|    |     
--2----5---
|    |    |
|    1    |
|    |    |
-----------


------     
|    |     
3    |     
|    |     
--4---
|    |
5    |
|    |
------

EDIT:


Clifford Torus

--1---
|    |
2    2
|    | 
--1---

EDIT:
Found a youtube video that explains the Angular Defecit/Angular Surplus floorplan better.

www.youtube.com/watch?v=kEB11PQ9Eo8#t=0m42s