Formulas for programming Poincare-disk tiling

[Drachenbauer]

Hello

I want to create this Poincare-disk-tiling out of hexagons and octagons in my game-programming software Godot:
-each octagon is fully surrounded by 8 hexagons
-each hexagon is surrounded by an alternating pattern of 3 hexagons and 3 octagons
I want 2 versions: like in the image (+ some 90° rotations) and with an octagon (In the rotation of a stop-sign) in the center.

And i want to create another tiling, where the order of hexagons and octagons is reversed:
-each hexagon is fully surrounded by 6 octagons
-each octagon is surrounded by an alternating pattern of 4 hexagons and 4 octagons
-Orientations of center-polygons as described above

in both tilings each corner is shared by 3 polygons

Which formulas do i need for these specific tilings?

A picture of the first tiling (found on the web):

 

[Drachenbauer]

This is the seccond tiling, that i want to create, i made it with the tool, that was used, where i found the first image.
But until i found the tool, the editing-timeframe for the startpost was over, so i added it here.
It already has a fitting orientation for what i want to make.

 

[mmm4444bot]

the editing-timeframe for the startpost was over, so i added it here

All posts have a 5-minute limit for editing. After that, you may add, change or clarify content with additional posts. In some instances, you may also contact a moderator by private conversation to request alterations (to be done at the moderator's discretion).

Thanks for letting us know that you were able to resolve your original question.

 

[Cubist]

Beautiful images . They seem to be from this website:-
https://www.plunk.org/~hatch/HyperbolicTesselations/

 

[Drachenbauer]

But i still need the formulas for these tilings to recreate them in a game-making-tool called godot.
I want to make a top-down rpg and a maze, that play in such tiled hyperbolic worlds.

The top-down rpg should play on the first tiling.
The player starts at the town hall of the main town.
The town-hall is an octagon tile and the center of the entire game-world.
It should contain a storage for not used items, a station to switch between the classes and a station to manage guilds.
The 8 surrounding octagon tiles should be stores for equipment of 8 different adventurer classes.
The hexagons in between them should be the path-ways through the town.

The maze should play on the second tiling and the hexagons should be massive pillars and on some edges between two octagons should be thin walls in a random generated pattern, where every two octagons can be reached through just one specific path.