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Architech Haresh Lalvani, designed a similar system, using regular polygons at vertices to define angles, specified as integers corresponding to internal angles.

The four figures below shows the identical tiles in Lalvani's internal angle indexing, and polytile turn angle indexing. The conversion is turn-angle-index = p/2 - internal-angle-index. You can see for rhombi, the indexing are complimentary, acute and obtuse angles switch values. Lalvani's examples don't give the sequence as a code like polytile notation, but instead offers a global ID index for each when positioned in a tiling.

US Patent 5775040

Polytiles: 8:1.3^2; 10:2.3^2; 12:2.1.3^2

Polytiles: 8:2.3.-1^2; 10:2.4.-1^2; 12:2.5.-1^2; 14:2.6.-1^2

Polytiles: 10:; 12:; 14:

Polytile 10:3.1.3.-1.-1^2