Four octatiling: with stellaocti -1.2^8, -2.3^8, stellatetrus -1.3^4 with squares and spinners -2.3.1^4 and -3.3.2^4 in the gaps. All are topological truncated square tilings.
More periodic octatilings
More octatilings - equilateral polygons, turn angles multiples of 45 degrees.
A little snake octatile, -2.3.2.1^2 self-tiles the plane with 2 orientation. It is topologically a hexagonal tiling, as shown right, by applying dual operation twice.
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Here is an octatile, 24-sided, 1.1.1.-1.-1.-3.3.1.1.3.-1.-1.-1.-1.3.1.1.3.-3.-1.-1.1.1.1, shaped like a starship enterprise, and it can self-tesselate the plane.
Surprisingly a tiling of forward facing enterprise, with funny purple gaps does something weird. A topological simplification (by applying dual operator twice) makes a heptagonal tiling with triangles. I don't actually have a name for this arrangement. Third image is single dual.
I found I can make the funny tiling from a trihexagonal tiling, by removing one edge between a triangle and hexagon, which expands each hexagon into heptagons. And apply dual twice adjusts the geometry like the enterprise tiling.