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