In each case, modifications along hexagon-edges were made using equilateral triangles. Every segment in this tessellation has equal length, also, which required trisection of the original hexagons’ sides.
I suspect that this could be continued outward indefinitely, as a radial and aperiodic tessellation, using only the four polygons you see, repeatedly, here. However, I have no proof of this.
This tessellation is made entirely of octagons. Half of them are regular, while the other half are equilateral and tetraconcave.