Coordinates of regular polygons (radius 1)

Coordinates of regular polygons from 3 (triangle) to 20 (icosagon) edges.

By Xenos — Check also the blog version and the other demos I made

3 polygon

Coordinates
First point ↺
1 0
-0.5 -0.866
-0.5 0.866
45° rotated
First point ↺
0.707 -0.707
-0.966 -0.259
0.259 0.966
90° rotated
First point ↺
0 -1
-0.866 0.5
0.866 0.5

4 polygon

Coordinates
First point ↺
1 0
0 -1
-1 -0
-0 1
45° rotated
First point ↺
0.707 -0.707
-0.707 -0.707
-0.707 0.707
0.707 0.707
90° rotated
First point ↺
0 -1
-1 -0
-0 1
1 0

5 polygon

Coordinates
First point ↺
1 0
0.309 -0.951
-0.809 -0.588
-0.809 0.588
0.309 0.951
45° rotated
First point ↺
0.707 -0.707
-0.454 -0.891
-0.988 0.156
-0.156 0.988
0.891 0.454
90° rotated
First point ↺
0 -1
-0.951 -0.309
-0.588 0.809
0.588 0.809
0.951 -0.309

6 polygon

Coordinates
First point ↺
1 0
0.5 -0.866
-0.5 -0.866
-1 -0
-0.5 0.866
0.5 0.866
45° rotated
First point ↺
0.707 -0.707
-0.259 -0.966
-0.966 -0.259
-0.707 0.707
0.259 0.966
0.966 0.259
90° rotated
First point ↺
0 -1
-0.866 -0.5
-0.866 0.5
-0 1
0.866 0.5
0.866 -0.5

7 polygon

Coordinates
First point ↺
1 0
0.623 -0.782
-0.223 -0.975
-0.901 -0.434
-0.901 0.434
-0.223 0.975
0.623 0.782
45° rotated
First point ↺
0.707 -0.707
-0.112 -0.994
-0.847 -0.532
-0.944 0.33
-0.33 0.944
0.532 0.847
0.994 0.112
90° rotated
First point ↺
0 -1
-0.782 -0.623
-0.975 0.223
-0.434 0.901
0.434 0.901
0.975 0.223
0.782 -0.623

8 polygon

Coordinates
First point ↺
1 0
0.707 -0.707
0 -1
-0.707 -0.707
-1 -0
-0.707 0.707
-0 1
0.707 0.707
45° rotated
First point ↺
0.707 -0.707
0 -1
-0.707 -0.707
-1 -0
-0.707 0.707
-0 1
0.707 0.707
1 0
90° rotated
First point ↺
0 -1
-0.707 -0.707
-1 -0
-0.707 0.707
-0 1
0.707 0.707
1 0
0.707 -0.707

9 polygon

Coordinates
First point ↺
1 0
0.766 -0.643
0.174 -0.985
-0.5 -0.866
-0.94 -0.342
-0.94 0.342
-0.5 0.866
0.174 0.985
0.766 0.643
45° rotated
First point ↺
0.707 -0.707
0.087 -0.996
-0.574 -0.819
-0.966 -0.259
-0.906 0.423
-0.423 0.906
0.259 0.966
0.819 0.574
0.996 -0.087
90° rotated
First point ↺
0 -1
-0.643 -0.766
-0.985 -0.174
-0.866 0.5
-0.342 0.94
0.342 0.94
0.866 0.5
0.985 -0.174
0.643 -0.766

10 polygon

Coordinates
First point ↺
1 0
0.809 -0.588
0.309 -0.951
-0.309 -0.951
-0.809 -0.588
-1 -0
-0.809 0.588
-0.309 0.951
0.309 0.951
0.809 0.588
45° rotated
First point ↺
0.707 -0.707
0.156 -0.988
-0.454 -0.891
-0.891 -0.454
-0.988 0.156
-0.707 0.707
-0.156 0.988
0.454 0.891
0.891 0.454
0.988 -0.156
90° rotated
First point ↺
0 -1
-0.588 -0.809
-0.951 -0.309
-0.951 0.309
-0.588 0.809
-0 1
0.588 0.809
0.951 0.309
0.951 -0.309
0.588 -0.809

11 polygon

Coordinates
First point ↺
1 0
0.841 -0.541
0.415 -0.91
-0.142 -0.99
-0.655 -0.756
-0.959 -0.282
-0.959 0.282
-0.655 0.756
-0.142 0.99
0.415 0.91
0.841 0.541
45° rotated
First point ↺
0.707 -0.707
0.213 -0.977
-0.349 -0.937
-0.801 -0.599
-0.997 -0.071
-0.878 0.479
-0.479 0.878
0.071 0.997
0.599 0.801
0.937 0.349
0.977 -0.213
90° rotated
First point ↺
0 -1
-0.541 -0.841
-0.91 -0.415
-0.99 0.142
-0.756 0.655
-0.282 0.959
0.282 0.959
0.756 0.655
0.99 0.142
0.91 -0.415
0.541 -0.841

12 polygon

Coordinates
First point ↺
1 0
0.866 -0.5
0.5 -0.866
0 -1
-0.5 -0.866
-0.866 -0.5
-1 -0
-0.866 0.5
-0.5 0.866
-0 1
0.5 0.866
0.866 0.5
45° rotated
First point ↺
0.707 -0.707
0.259 -0.966
-0.259 -0.966
-0.707 -0.707
-0.966 -0.259
-0.966 0.259
-0.707 0.707
-0.259 0.966
0.259 0.966
0.707 0.707
0.966 0.259
0.966 -0.259
90° rotated
First point ↺
0 -1
-0.5 -0.866
-0.866 -0.5
-1 -0
-0.866 0.5
-0.5 0.866
-0 1
0.5 0.866
0.866 0.5
1 0
0.866 -0.5
0.5 -0.866

13 polygon

Coordinates
First point ↺
1 0
0.885 -0.465
0.568 -0.823
0.121 -0.993
-0.355 -0.935
-0.749 -0.663
-0.971 -0.239
-0.971 0.239
-0.749 0.663
-0.355 0.935
0.121 0.993
0.568 0.823
0.885 0.465
45° rotated
First point ↺
0.707 -0.707
0.298 -0.955
-0.18 -0.984
-0.617 -0.787
-0.912 -0.41
-0.998 0.06
-0.856 0.517
-0.517 0.856
-0.06 0.998
0.41 0.912
0.787 0.617
0.984 0.18
0.955 -0.298
90° rotated
First point ↺
0 -1
-0.465 -0.885
-0.823 -0.568
-0.993 -0.121
-0.935 0.355
-0.663 0.749
-0.239 0.971
0.239 0.971
0.663 0.749
0.935 0.355
0.993 -0.121
0.823 -0.568
0.465 -0.885

14 polygon

Coordinates
First point ↺
1 0
0.901 -0.434
0.623 -0.782
0.223 -0.975
-0.223 -0.975
-0.623 -0.782
-0.901 -0.434
-1 -0
-0.901 0.434
-0.623 0.782
-0.223 0.975
0.223 0.975
0.623 0.782
0.901 0.434
45° rotated
First point ↺
0.707 -0.707
0.33 -0.944
-0.112 -0.994
-0.532 -0.847
-0.847 -0.532
-0.994 -0.112
-0.944 0.33
-0.707 0.707
-0.33 0.944
0.112 0.994
0.532 0.847
0.847 0.532
0.994 0.112
0.944 -0.33
90° rotated
First point ↺
0 -1
-0.434 -0.901
-0.782 -0.623
-0.975 -0.223
-0.975 0.223
-0.782 0.623
-0.434 0.901
-0 1
0.434 0.901
0.782 0.623
0.975 0.223
0.975 -0.223
0.782 -0.623
0.434 -0.901

15 polygon

Coordinates
First point ↺
1 0
0.914 -0.407
0.669 -0.743
0.309 -0.951
-0.105 -0.995
-0.5 -0.866
-0.809 -0.588
-0.978 -0.208
-0.978 0.208
-0.809 0.588
-0.5 0.866
-0.105 0.995
0.309 0.951
0.669 0.743
0.914 0.407
45° rotated
First point ↺
0.707 -0.707
0.358 -0.934
-0.052 -0.999
-0.454 -0.891
-0.777 -0.629
-0.966 -0.259
-0.988 0.156
-0.839 0.545
-0.545 0.839
-0.156 0.988
0.259 0.966
0.629 0.777
0.891 0.454
0.999 0.052
0.934 -0.358
90° rotated
First point ↺
0 -1
-0.407 -0.914
-0.743 -0.669
-0.951 -0.309
-0.995 0.105
-0.866 0.5
-0.588 0.809
-0.208 0.978
0.208 0.978
0.588 0.809
0.866 0.5
0.995 0.105
0.951 -0.309
0.743 -0.669
0.407 -0.914

16 polygon

Coordinates
First point ↺
1 0
0.924 -0.383
0.707 -0.707
0.383 -0.924
0 -1
-0.383 -0.924
-0.707 -0.707
-0.924 -0.383
-1 -0
-0.924 0.383
-0.707 0.707
-0.383 0.924
-0 1
0.383 0.924
0.707 0.707
0.924 0.383
45° rotated
First point ↺
0.707 -0.707
0.383 -0.924
0 -1
-0.383 -0.924
-0.707 -0.707
-0.924 -0.383
-1 -0
-0.924 0.383
-0.707 0.707
-0.383 0.924
-0 1
0.383 0.924
0.707 0.707
0.924 0.383
1 0
0.924 -0.383
90° rotated
First point ↺
0 -1
-0.383 -0.924
-0.707 -0.707
-0.924 -0.383
-1 -0
-0.924 0.383
-0.707 0.707
-0.383 0.924
-0 1
0.383 0.924
0.707 0.707
0.924 0.383
1 0
0.924 -0.383
0.707 -0.707
0.383 -0.924

17 polygon

Coordinates
First point ↺
1 0
0.932 -0.361
0.739 -0.674
0.446 -0.895
0.092 -0.996
-0.274 -0.962
-0.603 -0.798
-0.85 -0.526
-0.983 -0.184
-0.983 0.184
-0.85 0.526
-0.603 0.798
-0.274 0.962
0.092 0.996
0.446 0.895
0.739 0.674
0.932 0.361
45° rotated
First point ↺
0.707 -0.707
0.404 -0.915
0.046 -0.999
-0.318 -0.948
-0.639 -0.769
-0.874 -0.487
-0.99 -0.138
-0.973 0.229
-0.825 0.565
-0.565 0.825
-0.229 0.973
0.138 0.99
0.487 0.874
0.769 0.639
0.948 0.318
0.999 -0.046
0.915 -0.404
90° rotated
First point ↺
0 -1
-0.361 -0.932
-0.674 -0.739
-0.895 -0.446
-0.996 -0.092
-0.962 0.274
-0.798 0.603
-0.526 0.85
-0.184 0.983
0.184 0.983
0.526 0.85
0.798 0.603
0.962 0.274
0.996 -0.092
0.895 -0.446
0.674 -0.739
0.361 -0.932

18 polygon

Coordinates
First point ↺
1 0
0.94 -0.342
0.766 -0.643
0.5 -0.866
0.174 -0.985
-0.174 -0.985
-0.5 -0.866
-0.766 -0.643
-0.94 -0.342
-1 -0
-0.94 0.342
-0.766 0.643
-0.5 0.866
-0.174 0.985
0.174 0.985
0.5 0.866
0.766 0.643
0.94 0.342
45° rotated
First point ↺
0.707 -0.707
0.423 -0.906
0.087 -0.996
-0.259 -0.966
-0.574 -0.819
-0.819 -0.574
-0.966 -0.259
-0.996 0.087
-0.906 0.423
-0.707 0.707
-0.423 0.906
-0.087 0.996
0.259 0.966
0.574 0.819
0.819 0.574
0.966 0.259
0.996 -0.087
0.906 -0.423
90° rotated
First point ↺
0 -1
-0.342 -0.94
-0.643 -0.766
-0.866 -0.5
-0.985 -0.174
-0.985 0.174
-0.866 0.5
-0.643 0.766
-0.342 0.94
-0 1
0.342 0.94
0.643 0.766
0.866 0.5
0.985 0.174
0.985 -0.174
0.866 -0.5
0.643 -0.766
0.342 -0.94

19 polygon

Coordinates
First point ↺
1 0
0.946 -0.325
0.789 -0.614
0.547 -0.837
0.245 -0.969
-0.083 -0.997
-0.402 -0.916
-0.677 -0.736
-0.879 -0.476
-0.986 -0.165
-0.986 0.165
-0.879 0.476
-0.677 0.736
-0.402 0.916
-0.083 0.997
0.245 0.969
0.547 0.837
0.789 0.614
0.946 0.325
45° rotated
First point ↺
0.707 -0.707
0.439 -0.898
0.124 -0.992
-0.205 -0.979
-0.512 -0.859
-0.763 -0.646
-0.932 -0.364
-0.999 -0.041
-0.958 0.285
-0.814 0.581
-0.581 0.814
-0.285 0.958
0.041 0.999
0.364 0.932
0.646 0.763
0.859 0.512
0.979 0.205
0.992 -0.124
0.898 -0.439
90° rotated
First point ↺
0 -1
-0.325 -0.946
-0.614 -0.789
-0.837 -0.547
-0.969 -0.245
-0.997 0.083
-0.916 0.402
-0.736 0.677
-0.476 0.879
-0.165 0.986
0.165 0.986
0.476 0.879
0.736 0.677
0.916 0.402
0.997 0.083
0.969 -0.245
0.837 -0.547
0.614 -0.789
0.325 -0.946

20 polygon

Coordinates
First point ↺
1 0
0.951 -0.309
0.809 -0.588
0.588 -0.809
0.309 -0.951
0 -1
-0.309 -0.951
-0.588 -0.809
-0.809 -0.588
-0.951 -0.309
-1 -0
-0.951 0.309
-0.809 0.588
-0.588 0.809
-0.309 0.951
-0 1
0.309 0.951
0.588 0.809
0.809 0.588
0.951 0.309
45° rotated
First point ↺
0.707 -0.707
0.454 -0.891
0.156 -0.988
-0.156 -0.988
-0.454 -0.891
-0.707 -0.707
-0.891 -0.454
-0.988 -0.156
-0.988 0.156
-0.891 0.454
-0.707 0.707
-0.454 0.891
-0.156 0.988
0.156 0.988
0.454 0.891
0.707 0.707
0.891 0.454
0.988 0.156
0.988 -0.156
0.891 -0.454
90° rotated
First point ↺
0 -1
-0.309 -0.951
-0.588 -0.809
-0.809 -0.588
-0.951 -0.309
-1 -0
-0.951 0.309
-0.809 0.588
-0.588 0.809
-0.309 0.951
-0 1
0.309 0.951
0.588 0.809
0.809 0.588
0.951 0.309
1 0
0.951 -0.309
0.809 -0.588
0.588 -0.809
0.309 -0.951