The general concept of the Euclidean worlds mechanic is that you think you are going in one direction but you are actually going in the opposite of it. As a player you should be able to walk on opposite surfaces, shrink, enlarge, find hidden rooms. Things will not be as they seem and a bit confusing.
Based on MC Escher's art.
There are More Mechanics that are needed to be added, including floors that are walkable in any direction. Walking up a hill to reach the top, how it works can be viewed here: https://www.youtube.com/watch?v=kEB11PQ9Eo8
1. Windows should show random areas through them that make no sense.
2. Shapes should turn into other shapes by their negative form
3. Stairs in any direction
4. Upside down areas floating in the sky
Burning House/Shock:More about stealth and learning that tossing things through cracks in the wall will hit unexpected walls to confuse an enemy. Walking above/around/under enemies. Incorporating it into the wreckage, not beautiful like stairs on a castle.
Circus/Denial: Floating elements, elements implemented around denial. "Horror house" will be a huge long hallway but a short and small house.
Anger/Queensland: Will be whole rooms as part of the castle. Part of the maze, part of the forest and croquet grounds.
Hatter/Bargaining: Large Machines, mechanical operations that will need to be activated to work. Secret areas hidden around that the player will need to get there.
Hub/Depression: A "Dead" area with not a lot of action but with puzzle work and more walking and portal to places. It should be elements.
Jabberwock/Testing: Filled with action, will have running sequences, an integral part of the world itself, full rooms.
Red Chess/Acceptance: Part of the world.