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# Polytope of Type {14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,2}*56
if this polytope has a name.
Group : SmallGroup(56,12)
Rank : 3
Schlafli Type : {14,2}
Number of vertices, edges, etc : 14, 14, 2
Order of s0s1s2 : 14
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{14,2,2} of size 112
{14,2,3} of size 168
{14,2,4} of size 224
{14,2,5} of size 280
{14,2,6} of size 336
{14,2,7} of size 392
{14,2,8} of size 448
{14,2,9} of size 504
{14,2,10} of size 560
{14,2,11} of size 616
{14,2,12} of size 672
{14,2,13} of size 728
{14,2,14} of size 784
{14,2,15} of size 840
{14,2,16} of size 896
{14,2,17} of size 952
{14,2,18} of size 1008
{14,2,19} of size 1064
{14,2,20} of size 1120
{14,2,21} of size 1176
{14,2,22} of size 1232
{14,2,23} of size 1288
{14,2,24} of size 1344
{14,2,25} of size 1400
{14,2,26} of size 1456
{14,2,27} of size 1512
{14,2,28} of size 1568
{14,2,29} of size 1624
{14,2,30} of size 1680
{14,2,31} of size 1736
{14,2,32} of size 1792
{14,2,33} of size 1848
{14,2,34} of size 1904
{14,2,35} of size 1960
Vertex Figure Of :
{2,14,2} of size 112
{4,14,2} of size 224
{6,14,2} of size 336
{7,14,2} of size 392
{8,14,2} of size 448
{10,14,2} of size 560
{12,14,2} of size 672
{4,14,2} of size 784
{14,14,2} of size 784
{14,14,2} of size 784
{14,14,2} of size 784
{16,14,2} of size 896
{18,14,2} of size 1008
{20,14,2} of size 1120
{3,14,2} of size 1176
{6,14,2} of size 1176
{21,14,2} of size 1176
{22,14,2} of size 1232
{24,14,2} of size 1344
{3,14,2} of size 1344
{4,14,2} of size 1344
{4,14,2} of size 1344
{6,14,2} of size 1344
{6,14,2} of size 1344
{7,14,2} of size 1344
{8,14,2} of size 1344
{8,14,2} of size 1344
{8,14,2} of size 1344
{8,14,2} of size 1344
{26,14,2} of size 1456
{28,14,2} of size 1568
{28,14,2} of size 1568
{28,14,2} of size 1568
{8,14,2} of size 1568
{8,14,2} of size 1568
{4,14,2} of size 1568
{30,14,2} of size 1680
{32,14,2} of size 1792
{34,14,2} of size 1904
{35,14,2} of size 1960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {7,2}*28
7-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {28,2}*112, {14,4}*112
3-fold covers : {14,6}*168, {42,2}*168
4-fold covers : {28,4}*224, {56,2}*224, {14,8}*224
5-fold covers : {14,10}*280, {70,2}*280
6-fold covers : {14,12}*336, {28,6}*336a, {84,2}*336, {42,4}*336a
7-fold covers : {98,2}*392, {14,14}*392a, {14,14}*392c
8-fold covers : {56,4}*448a, {28,4}*448, {56,4}*448b, {28,8}*448a, {28,8}*448b, {112,2}*448, {14,16}*448
9-fold covers : {14,18}*504, {126,2}*504, {42,6}*504a, {42,6}*504b, {42,6}*504c
10-fold covers : {14,20}*560, {28,10}*560, {140,2}*560, {70,4}*560
11-fold covers : {14,22}*616, {154,2}*616
12-fold covers : {14,24}*672, {56,6}*672, {28,12}*672, {84,4}*672a, {168,2}*672, {42,8}*672, {28,6}*672, {42,6}*672, {42,4}*672
13-fold covers : {14,26}*728, {182,2}*728
14-fold covers : {196,2}*784, {98,4}*784, {14,28}*784a, {28,14}*784a, {28,14}*784b, {14,28}*784c
15-fold covers : {14,30}*840, {42,10}*840, {70,6}*840, {210,2}*840
16-fold covers : {56,4}*896a, {56,8}*896a, {56,8}*896b, {28,8}*896a, {56,8}*896c, {56,8}*896d, {112,4}*896a, {112,4}*896b, {28,4}*896, {56,4}*896b, {28,8}*896b, {28,16}*896a, {28,16}*896b, {224,2}*896, {14,32}*896
17-fold covers : {14,34}*952, {238,2}*952
18-fold covers : {14,36}*1008, {28,18}*1008a, {252,2}*1008, {126,4}*1008a, {84,6}*1008a, {42,12}*1008a, {42,12}*1008b, {84,6}*1008b, {84,6}*1008c, {42,12}*1008c, {28,4}*1008, {42,4}*1008, {28,6}*1008
19-fold covers : {14,38}*1064, {266,2}*1064
20-fold covers : {14,40}*1120, {56,10}*1120, {28,20}*1120, {140,4}*1120, {280,2}*1120, {70,8}*1120
21-fold covers : {98,6}*1176, {294,2}*1176, {14,42}*1176a, {14,42}*1176b, {42,14}*1176b, {42,14}*1176c
22-fold covers : {28,22}*1232, {14,44}*1232, {308,2}*1232, {154,4}*1232
23-fold covers : {14,46}*1288, {322,2}*1288
24-fold covers : {14,48}*1344, {112,6}*1344, {28,12}*1344a, {28,24}*1344a, {56,12}*1344a, {28,24}*1344b, {56,12}*1344b, {168,4}*1344a, {84,4}*1344a, {168,4}*1344b, {84,8}*1344a, {84,8}*1344b, {336,2}*1344, {42,16}*1344, {28,12}*1344b, {28,6}*1344e, {84,6}*1344a, {42,12}*1344a, {42,6}*1344, {56,6}*1344b, {56,6}*1344c, {84,6}*1344b, {28,12}*1344c, {42,12}*1344b, {84,4}*1344b, {42,4}*1344b, {84,4}*1344c, {42,8}*1344b, {42,8}*1344c
25-fold covers : {14,50}*1400, {350,2}*1400, {70,10}*1400a, {70,10}*1400b, {70,10}*1400c
26-fold covers : {28,26}*1456, {14,52}*1456, {364,2}*1456, {182,4}*1456
27-fold covers : {14,54}*1512, {378,2}*1512, {42,18}*1512a, {42,6}*1512a, {126,6}*1512a, {126,6}*1512b, {42,18}*1512b, {42,6}*1512b, {42,6}*1512c, {42,6}*1512d
28-fold covers : {196,4}*1568, {392,2}*1568, {98,8}*1568, {14,56}*1568a, {56,14}*1568a, {56,14}*1568b, {28,28}*1568a, {28,28}*1568c, {14,56}*1568c
29-fold covers : {14,58}*1624, {406,2}*1624
30-fold covers : {14,60}*1680, {28,30}*1680a, {42,20}*1680a, {84,10}*1680, {70,12}*1680, {140,6}*1680a, {420,2}*1680, {210,4}*1680a
31-fold covers : {14,62}*1736, {434,2}*1736
32-fold covers : {56,8}*1792a, {28,8}*1792a, {56,8}*1792b, {56,4}*1792a, {56,8}*1792c, {56,8}*1792d, {28,16}*1792a, {112,4}*1792a, {28,16}*1792b, {112,4}*1792b, {112,8}*1792a, {56,16}*1792a, {112,8}*1792b, {56,16}*1792b, {56,16}*1792c, {112,8}*1792c, {112,8}*1792d, {56,16}*1792d, {56,16}*1792e, {112,8}*1792e, {112,8}*1792f, {56,16}*1792f, {28,32}*1792a, {224,4}*1792a, {28,32}*1792b, {224,4}*1792b, {28,4}*1792, {56,4}*1792b, {28,8}*1792b, {28,8}*1792c, {56,8}*1792e, {56,4}*1792c, {56,4}*1792d, {28,8}*1792d, {56,8}*1792f, {56,8}*1792g, {56,8}*1792h, {14,64}*1792, {448,2}*1792
33-fold covers : {42,22}*1848, {14,66}*1848, {154,6}*1848, {462,2}*1848
34-fold covers : {28,34}*1904, {14,68}*1904, {476,2}*1904, {238,4}*1904
35-fold covers : {98,10}*1960, {490,2}*1960, {14,70}*1960a, {14,70}*1960b, {70,14}*1960b, {70,14}*1960c
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);;
s2 := (15,16);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2,
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(16)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s1 := Sym(16)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);
s2 := Sym(16)!(15,16);
poly := sub<Sym(16)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, 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 >;

```

to this polytope