Polytope of Type {7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7}*14
Also Known As : heptagon, {7}. if this polytope has another name.
Group : SmallGroup(14,1)
Rank : 2
Schlafli Type : {7}
Number of vertices, edges, etc : 7, 7
Order of s0s1 : 7
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2} of size 28
   {7,14} of size 196
   {7,3} of size 336
   {7,4} of size 336
   {7,6} of size 336
   {7,7} of size 336
   {7,8} of size 336
   {7,8} of size 336
   {7,3} of size 504
   {7,7} of size 504
   {7,7} of size 504
   {7,9} of size 504
   {7,9} of size 504
   {7,9} of size 504
   {7,4} of size 672
   {7,6} of size 672
   {7,6} of size 672
   {7,8} of size 672
   {7,8} of size 672
   {7,14} of size 672
   {7,4} of size 896
   {7,7} of size 896
   {7,3} of size 1008
   {7,6} of size 1008
   {7,6} of size 1008
   {7,7} of size 1008
   {7,7} of size 1008
   {7,9} of size 1008
   {7,9} of size 1008
   {7,9} of size 1008
   {7,14} of size 1008
   {7,14} of size 1008
   {7,14} of size 1008
   {7,14} of size 1008
   {7,18} of size 1008
   {7,18} of size 1008
   {7,18} of size 1008
   {7,18} of size 1008
   {7,18} of size 1008
   {7,18} of size 1008
   {7,3} of size 1092
   {7,6} of size 1092
   {7,7} of size 1092
   {7,7} of size 1092
   {7,7} of size 1092
   {7,7} of size 1092
   {7,13} of size 1092
   {7,13} of size 1092
   {7,13} of size 1092
   {7,6} of size 1344
   {7,8} of size 1344
   {7,12} of size 1344
   {7,16} of size 1344
   {7,16} of size 1344
   {7,28} of size 1344
   {7,14} of size 1372
   {7,4} of size 1792
   {7,4} of size 1792
   {7,7} of size 1792
   {7,7} of size 1792
   {7,7} of size 1792
   {7,8} of size 1792
   {7,8} of size 1792
   {7,8} of size 1792
   {7,8} of size 1792
   {7,14} of size 1792
   {7,14} of size 1792
   {7,14} of size 1792
   {7,4} of size 1792
   {7,14} of size 1792
Vertex Figure Of :
   {2,7} of size 28
   {14,7} of size 196
   {3,7} of size 336
   {4,7} of size 336
   {6,7} of size 336
   {7,7} of size 336
   {8,7} of size 336
   {8,7} of size 336
   {3,7} of size 504
   {7,7} of size 504
   {7,7} of size 504
   {9,7} of size 504
   {9,7} of size 504
   {9,7} of size 504
   {4,7} of size 672
   {6,7} of size 672
   {6,7} of size 672
   {8,7} of size 672
   {8,7} of size 672
   {14,7} of size 672
   {4,7} of size 896
   {7,7} of size 896
   {3,7} of size 1008
   {6,7} of size 1008
   {6,7} of size 1008
   {7,7} of size 1008
   {7,7} of size 1008
   {9,7} of size 1008
   {9,7} of size 1008
   {9,7} of size 1008
   {14,7} of size 1008
   {14,7} of size 1008
   {14,7} of size 1008
   {14,7} of size 1008
   {18,7} of size 1008
   {18,7} of size 1008
   {18,7} of size 1008
   {18,7} of size 1008
   {18,7} of size 1008
   {18,7} of size 1008
   {3,7} of size 1092
   {6,7} of size 1092
   {7,7} of size 1092
   {7,7} of size 1092
   {7,7} of size 1092
   {7,7} of size 1092
   {13,7} of size 1092
   {13,7} of size 1092
   {13,7} of size 1092
   {6,7} of size 1344
   {8,7} of size 1344
   {12,7} of size 1344
   {16,7} of size 1344
   {16,7} of size 1344
   {28,7} of size 1344
   {14,7} of size 1372
   {4,7} of size 1792
   {4,7} of size 1792
   {7,7} of size 1792
   {7,7} of size 1792
   {7,7} of size 1792
   {8,7} of size 1792
   {8,7} of size 1792
   {8,7} of size 1792
   {8,7} of size 1792
   {14,7} of size 1792
   {14,7} of size 1792
   {14,7} of size 1792
   {4,7} of size 1792
   {14,7} of size 1792
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14}*28
   3-fold covers : {21}*42
   4-fold covers : {28}*56
   5-fold covers : {35}*70
   6-fold covers : {42}*84
   7-fold covers : {49}*98
   8-fold covers : {56}*112
   9-fold covers : {63}*126
   10-fold covers : {70}*140
   11-fold covers : {77}*154
   12-fold covers : {84}*168
   13-fold covers : {91}*182
   14-fold covers : {98}*196
   15-fold covers : {105}*210
   16-fold covers : {112}*224
   17-fold covers : {119}*238
   18-fold covers : {126}*252
   19-fold covers : {133}*266
   20-fold covers : {140}*280
   21-fold covers : {147}*294
   22-fold covers : {154}*308
   23-fold covers : {161}*322
   24-fold covers : {168}*336
   25-fold covers : {175}*350
   26-fold covers : {182}*364
   27-fold covers : {189}*378
   28-fold covers : {196}*392
   29-fold covers : {203}*406
   30-fold covers : {210}*420
   31-fold covers : {217}*434
   32-fold covers : {224}*448
   33-fold covers : {231}*462
   34-fold covers : {238}*476
   35-fold covers : {245}*490
   36-fold covers : {252}*504
   37-fold covers : {259}*518
   38-fold covers : {266}*532
   39-fold covers : {273}*546
   40-fold covers : {280}*560
   41-fold covers : {287}*574
   42-fold covers : {294}*588
   43-fold covers : {301}*602
   44-fold covers : {308}*616
   45-fold covers : {315}*630
   46-fold covers : {322}*644
   47-fold covers : {329}*658
   48-fold covers : {336}*672
   49-fold covers : {343}*686
   50-fold covers : {350}*700
   51-fold covers : {357}*714
   52-fold covers : {364}*728
   53-fold covers : {371}*742
   54-fold covers : {378}*756
   55-fold covers : {385}*770
   56-fold covers : {392}*784
   57-fold covers : {399}*798
   58-fold covers : {406}*812
   59-fold covers : {413}*826
   60-fold covers : {420}*840
   61-fold covers : {427}*854
   62-fold covers : {434}*868
   63-fold covers : {441}*882
   64-fold covers : {448}*896
   65-fold covers : {455}*910
   66-fold covers : {462}*924
   67-fold covers : {469}*938
   68-fold covers : {476}*952
   69-fold covers : {483}*966
   70-fold covers : {490}*980
   71-fold covers : {497}*994
   72-fold covers : {504}*1008
   73-fold covers : {511}*1022
   74-fold covers : {518}*1036
   75-fold covers : {525}*1050
   76-fold covers : {532}*1064
   77-fold covers : {539}*1078
   78-fold covers : {546}*1092
   79-fold covers : {553}*1106
   80-fold covers : {560}*1120
   81-fold covers : {567}*1134
   82-fold covers : {574}*1148
   83-fold covers : {581}*1162
   84-fold covers : {588}*1176
   85-fold covers : {595}*1190
   86-fold covers : {602}*1204
   87-fold covers : {609}*1218
   88-fold covers : {616}*1232
   89-fold covers : {623}*1246
   90-fold covers : {630}*1260
   91-fold covers : {637}*1274
   92-fold covers : {644}*1288
   93-fold covers : {651}*1302
   94-fold covers : {658}*1316
   95-fold covers : {665}*1330
   96-fold covers : {672}*1344
   97-fold covers : {679}*1358
   98-fold covers : {686}*1372
   99-fold covers : {693}*1386
   100-fold covers : {700}*1400
   101-fold covers : {707}*1414
   102-fold covers : {714}*1428
   103-fold covers : {721}*1442
   104-fold covers : {728}*1456
   105-fold covers : {735}*1470
   106-fold covers : {742}*1484
   107-fold covers : {749}*1498
   108-fold covers : {756}*1512
   109-fold covers : {763}*1526
   110-fold covers : {770}*1540
   111-fold covers : {777}*1554
   112-fold covers : {784}*1568
   113-fold covers : {791}*1582
   114-fold covers : {798}*1596
   115-fold covers : {805}*1610
   116-fold covers : {812}*1624
   117-fold covers : {819}*1638
   118-fold covers : {826}*1652
   119-fold covers : {833}*1666
   120-fold covers : {840}*1680
   121-fold covers : {847}*1694
   122-fold covers : {854}*1708
   123-fold covers : {861}*1722
   124-fold covers : {868}*1736
   125-fold covers : {875}*1750
   126-fold covers : {882}*1764
   127-fold covers : {889}*1778
   128-fold covers : {896}*1792
   129-fold covers : {903}*1806
   130-fold covers : {910}*1820
   131-fold covers : {917}*1834
   132-fold covers : {924}*1848
   133-fold covers : {931}*1862
   134-fold covers : {938}*1876
   135-fold covers : {945}*1890
   136-fold covers : {952}*1904
   137-fold covers : {959}*1918
   138-fold covers : {966}*1932
   139-fold covers : {973}*1946
   140-fold covers : {980}*1960
   141-fold covers : {987}*1974
   142-fold covers : {994}*1988
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(7)!(2,3)(4,5)(6,7);
s1 := Sym(7)!(1,2)(3,4)(5,6);
poly := sub<Sym(7)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope