Tilings not constructible by straightedge and compass

data0/AJL6 data0/GHA data0/CR20 data0/CR16 data0/CR13 data8/PG180 data12/P136 data12/P164 data12/P170 data12/P166 data12/P167 data18/RIG2 data146/F417D data146/F415D data147/F4L data147/F254P data147/F96 data157/R7A data157/C7 data157/R7B data158/B124 data160/L1 data160/P120 data162/P073 data168/F142 data169/P165 data169/P108 data169/FIG7 data169/FIG10 data169/FIG5 data172/B125 data172/EGY1217 data173/B125L data174/FIG4 data175/AJL1 data175/AJL2 data175/MEIN1 data175/B168 data177/J43C data178/T19 data178/T23 data178/T22 data180/FIG8 data181/V5P125 data182/IND0724 data184/AJL1 data184/B123 data185/AJL19 data186/IS1 data186/H3 data186/B136 data187/F4 data187/FIG12 data188/FIG5A data188/FIG5 data188/FIG2 data188/FIG4 data189/IRA0633 data191/FIG5 data193/IS14F6 data193/IS14F1 data193/IS14F4 data193/IS14F3 data193/IS14F2 data193/IS14F5 data194/IS14F7 data194/IS14F9 data194/IS14F8 data194/IS14F13 data194/IS14F12 data194/IS14F15 data194/IS14F10 data194/IS14F11 data195/Q1 data195/B167R data196/P144 data197/MAU data197/B170 data197/IND0724 data198/BR1 data203/B032A data203/P120 data204/P136 data204/VA2 data208/FE7 data209/BON4 data210/BON13 data211/BON21 data211/BON9A data212/BON51 data212/BON102 data212/BON121 data212/BON99 data212/BON100 data212/BON109 data212/BON101 data215/MB2
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.