How do I design an exact circle tiling, like the one in this paper (first page, Figure 2, third column) but with the exact mathematical proportions?
Note that all tiles are identical.
Answer
The central trick is that the entire figure is composed of eighteen identical 60° arcs, which are rotated by simple angles. All you have to do is create these arcs, rotate them, and put them into place (with snapping):

Create a circle using the Create circles, ellipses, and arcs tool (hold Shift while dragging).

Duplicate it (Ctrl + D). I here make the duplicate red for better distinction.

Make it a 60° arc, either by dragging the handles (while pressing Ctrl) or by manually entering the value in the Create circles, ellipses, and arcs tool:

Activate Snapping, Snap to nodes or handles and Snap to cusp nodes.

Repeat the following twelve times:

Duplicate your arc.

Apply Object → Transform → Rotate by 30° as often as needed (or directly enter the correct value).

Position the new arc as needed such that it snaps. (Start with arcs adjacent to your original one to have a basis for snapping.)

Attribution
Source : Link , Question Author : Bruno Saramago Monteiro , Answer Author : Wrzlprmft