Polytope of Type {14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14}*28
Also Known As : 14-gon, {14}. if this polytope has another name.
Group : SmallGroup(28,3)
Rank : 2
Schlafli Type : {14}
Number of vertices, edges, etc : 14, 14
Order of s0s1 : 14
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{14,2} of size 56
{14,4} of size 112
{14,6} of size 168
{14,7} of size 196
{14,8} of size 224
{14,10} of size 280
{14,12} of size 336
{14,4} of size 392
{14,14} of size 392
{14,14} of size 392
{14,14} of size 392
{14,16} of size 448
{14,18} of size 504
{14,20} of size 560
{14,3} of size 588
{14,6} of size 588
{14,21} of size 588
{14,22} of size 616
{14,24} of size 672
{14,3} of size 672
{14,4} of size 672
{14,4} of size 672
{14,6} of size 672
{14,6} of size 672
{14,7} of size 672
{14,8} of size 672
{14,8} of size 672
{14,8} of size 672
{14,8} of size 672
{14,26} of size 728
{14,28} of size 784
{14,28} of size 784
{14,28} of size 784
{14,8} of size 784
{14,8} of size 784
{14,4} of size 784
{14,30} of size 840
{14,32} of size 896
{14,34} of size 952
{14,35} of size 980
{14,36} of size 1008
{14,3} of size 1008
{14,3} of size 1008
{14,7} of size 1008
{14,7} of size 1008
{14,7} of size 1008
{14,7} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,38} of size 1064
{14,40} of size 1120
{14,6} of size 1176
{14,6} of size 1176
{14,12} of size 1176
{14,42} of size 1176
{14,42} of size 1176
{14,42} of size 1176
{14,44} of size 1232
{14,46} of size 1288
{14,48} of size 1344
{14,6} of size 1344
{14,4} of size 1344
{14,6} of size 1344
{14,6} of size 1344
{14,8} of size 1344
{14,8} of size 1344
{14,14} of size 1344
{14,49} of size 1372
{14,7} of size 1372
{14,14} of size 1372
{14,50} of size 1400
{14,52} of size 1456
{14,54} of size 1512
{14,56} of size 1568
{14,56} of size 1568
{14,56} of size 1568
{14,8} of size 1568
{14,8} of size 1568
{14,8} of size 1568
{14,58} of size 1624
{14,60} of size 1680
{14,62} of size 1736
{14,9} of size 1764
{14,18} of size 1764
{14,63} of size 1764
{14,64} of size 1792
{14,4} of size 1792
{14,4} of size 1792
{14,7} of size 1792
{14,7} of size 1792
{14,7} of size 1792
{14,4} of size 1792
{14,4} of size 1792
{14,7} of size 1792
{14,66} of size 1848
{14,68} of size 1904
{14,20} of size 1960
{14,70} of size 1960
{14,70} of size 1960
{14,70} of size 1960
Vertex Figure Of :
{2,14} of size 56
{4,14} of size 112
{6,14} of size 168
{7,14} of size 196
{8,14} of size 224
{10,14} of size 280
{12,14} of size 336
{4,14} of size 392
{14,14} of size 392
{14,14} of size 392
{14,14} of size 392
{16,14} of size 448
{18,14} of size 504
{20,14} of size 560
{3,14} of size 588
{6,14} of size 588
{21,14} of size 588
{22,14} of size 616
{24,14} of size 672
{3,14} of size 672
{4,14} of size 672
{4,14} of size 672
{6,14} of size 672
{6,14} of size 672
{7,14} of size 672
{8,14} of size 672
{8,14} of size 672
{8,14} of size 672
{8,14} of size 672
{26,14} of size 728
{28,14} of size 784
{28,14} of size 784
{28,14} of size 784
{8,14} of size 784
{8,14} of size 784
{4,14} of size 784
{30,14} of size 840
{32,14} of size 896
{34,14} of size 952
{35,14} of size 980
{36,14} of size 1008
{3,14} of size 1008
{3,14} of size 1008
{7,14} of size 1008
{7,14} of size 1008
{7,14} of size 1008
{7,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{38,14} of size 1064
{40,14} of size 1120
{6,14} of size 1176
{6,14} of size 1176
{12,14} of size 1176
{42,14} of size 1176
{42,14} of size 1176
{42,14} of size 1176
{44,14} of size 1232
{46,14} of size 1288
{48,14} of size 1344
{6,14} of size 1344
{4,14} of size 1344
{6,14} of size 1344
{6,14} of size 1344
{8,14} of size 1344
{8,14} of size 1344
{14,14} of size 1344
{49,14} of size 1372
{7,14} of size 1372
{14,14} of size 1372
{50,14} of size 1400
{52,14} of size 1456
{54,14} of size 1512
{56,14} of size 1568
{56,14} of size 1568
{56,14} of size 1568
{8,14} of size 1568
{8,14} of size 1568
{8,14} of size 1568
{58,14} of size 1624
{60,14} of size 1680
{62,14} of size 1736
{9,14} of size 1764
{18,14} of size 1764
{63,14} of size 1764
{64,14} of size 1792
{4,14} of size 1792
{4,14} of size 1792
{7,14} of size 1792
{7,14} of size 1792
{7,14} of size 1792
{4,14} of size 1792
{4,14} of size 1792
{7,14} of size 1792
{66,14} of size 1848
{68,14} of size 1904
{20,14} of size 1960
{70,14} of size 1960
{70,14} of size 1960
{70,14} of size 1960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {7}*14
7-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {28}*56
3-fold covers : {42}*84
4-fold covers : {56}*112
5-fold covers : {70}*140
6-fold covers : {84}*168
7-fold covers : {98}*196
8-fold covers : {112}*224
9-fold covers : {126}*252
10-fold covers : {140}*280
11-fold covers : {154}*308
12-fold covers : {168}*336
13-fold covers : {182}*364
14-fold covers : {196}*392
15-fold covers : {210}*420
16-fold covers : {224}*448
17-fold covers : {238}*476
18-fold covers : {252}*504
19-fold covers : {266}*532
20-fold covers : {280}*560
21-fold covers : {294}*588
22-fold covers : {308}*616
23-fold covers : {322}*644
24-fold covers : {336}*672
25-fold covers : {350}*700
26-fold covers : {364}*728
27-fold covers : {378}*756
28-fold covers : {392}*784
29-fold covers : {406}*812
30-fold covers : {420}*840
31-fold covers : {434}*868
32-fold covers : {448}*896
33-fold covers : {462}*924
34-fold covers : {476}*952
35-fold covers : {490}*980
36-fold covers : {504}*1008
37-fold covers : {518}*1036
38-fold covers : {532}*1064
39-fold covers : {546}*1092
40-fold covers : {560}*1120
41-fold covers : {574}*1148
42-fold covers : {588}*1176
43-fold covers : {602}*1204
44-fold covers : {616}*1232
45-fold covers : {630}*1260
46-fold covers : {644}*1288
47-fold covers : {658}*1316
48-fold covers : {672}*1344
49-fold covers : {686}*1372
50-fold covers : {700}*1400
51-fold covers : {714}*1428
52-fold covers : {728}*1456
53-fold covers : {742}*1484
54-fold covers : {756}*1512
55-fold covers : {770}*1540
56-fold covers : {784}*1568
57-fold covers : {798}*1596
58-fold covers : {812}*1624
59-fold covers : {826}*1652
60-fold covers : {840}*1680
61-fold covers : {854}*1708
62-fold covers : {868}*1736
63-fold covers : {882}*1764
64-fold covers : {896}*1792
65-fold covers : {910}*1820
66-fold covers : {924}*1848
67-fold covers : {938}*1876
68-fold covers : {952}*1904
69-fold covers : {966}*1932
70-fold covers : {980}*1960
71-fold covers : {994}*1988
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(14)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s1 := Sym(14)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);
poly := sub<Sym(14)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope