Tilings not constructible by straightedge and compass

data0/AJL6 data12/P136 data12/P164 data12/P166 data12/P167 data12/P170 data146/F415D data146/F417D data147/F254P data147/F4L data147/F96 data157/C7 data157/R7A data157/R7B data158/B124 data160/L1 data160/P120 data162/P073 data168/F142 data169/FIG10 data169/FIG5 data169/FIG7 data169/P108 data169/P165 data172/B125 data172/EGY1217 data173/B125L data174/TUR0829 data175/B168 data175/MEIN1 data177/J43C data178/T19 data178/T22 data178/T23 data18/RIG2 data180/FIG8 data181/V5P125 data182/IND0724 data184/AJL1 data184/B123 data185/AJL19 data186/B136 data186/H3 data187/F4 data187/FIG12 data188/FIG2 data188/FIG4 data188/FIG5 data188/FIG5A data189/IRA0633 data191/FIG5 data195/B167R data195/Q1 data196/P144 data197/B170 data197/IND0724 data197/MAU data198/BR1 data203/B032A data203/P120 data204/P136 data204/VA2 data8/PG180
A regular (star) polygon is not constructible if the number of sides = 7, 9, 11, 13, 14, 18, 19, 21, 22, 23, 25, ... Hence we list them all here. The rest are almost certainly constructible. (We ignore modern inventions.)

Total number of patterns: 63