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# Polytope of Type {2,14}

Atlas Canonical Name : {2,14}*56
if this polytope has a name.
Group : SmallGroup(56,12)
Rank : 3
Schlafli Type : {2,14}
Number of vertices, edges, etc : 2, 14, 14
Order of s0s1s2 : 14
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,14,2} of size 112
{2,14,4} of size 224
{2,14,6} of size 336
{2,14,7} of size 392
{2,14,8} of size 448
{2,14,10} of size 560
{2,14,12} of size 672
{2,14,4} of size 784
{2,14,14} of size 784
{2,14,14} of size 784
{2,14,14} of size 784
{2,14,16} of size 896
{2,14,18} of size 1008
{2,14,20} of size 1120
{2,14,3} of size 1176
{2,14,6} of size 1176
{2,14,21} of size 1176
{2,14,22} of size 1232
{2,14,24} of size 1344
{2,14,3} of size 1344
{2,14,4} of size 1344
{2,14,4} of size 1344
{2,14,6} of size 1344
{2,14,6} of size 1344
{2,14,7} of size 1344
{2,14,8} of size 1344
{2,14,8} of size 1344
{2,14,8} of size 1344
{2,14,8} of size 1344
{2,14,26} of size 1456
{2,14,28} of size 1568
{2,14,28} of size 1568
{2,14,28} of size 1568
{2,14,8} of size 1568
{2,14,8} of size 1568
{2,14,4} of size 1568
{2,14,30} of size 1680
{2,14,32} of size 1792
{2,14,34} of size 1904
{2,14,35} of size 1960
Vertex Figure Of :
{2,2,14} of size 112
{3,2,14} of size 168
{4,2,14} of size 224
{5,2,14} of size 280
{6,2,14} of size 336
{7,2,14} of size 392
{8,2,14} of size 448
{9,2,14} of size 504
{10,2,14} of size 560
{11,2,14} of size 616
{12,2,14} of size 672
{13,2,14} of size 728
{14,2,14} of size 784
{15,2,14} of size 840
{16,2,14} of size 896
{17,2,14} of size 952
{18,2,14} of size 1008
{19,2,14} of size 1064
{20,2,14} of size 1120
{21,2,14} of size 1176
{22,2,14} of size 1232
{23,2,14} of size 1288
{24,2,14} of size 1344
{25,2,14} of size 1400
{26,2,14} of size 1456
{27,2,14} of size 1512
{28,2,14} of size 1568
{29,2,14} of size 1624
{30,2,14} of size 1680
{31,2,14} of size 1736
{32,2,14} of size 1792
{33,2,14} of size 1848
{34,2,14} of size 1904
{35,2,14} of size 1960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,7}*28
7-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,28}*112, {4,14}*112
3-fold covers : {6,14}*168, {2,42}*168
4-fold covers : {4,28}*224, {2,56}*224, {8,14}*224
5-fold covers : {10,14}*280, {2,70}*280
6-fold covers : {12,14}*336, {6,28}*336a, {2,84}*336, {4,42}*336a
7-fold covers : {2,98}*392, {14,14}*392a, {14,14}*392b
8-fold covers : {4,56}*448a, {4,28}*448, {4,56}*448b, {8,28}*448a, {8,28}*448b, {2,112}*448, {16,14}*448
9-fold covers : {18,14}*504, {2,126}*504, {6,42}*504a, {6,42}*504b, {6,42}*504c
10-fold covers : {20,14}*560, {10,28}*560, {2,140}*560, {4,70}*560
11-fold covers : {22,14}*616, {2,154}*616
12-fold covers : {24,14}*672, {6,56}*672, {12,28}*672, {4,84}*672a, {2,168}*672, {8,42}*672, {6,28}*672, {6,42}*672, {4,42}*672
13-fold covers : {26,14}*728, {2,182}*728
14-fold covers : {2,196}*784, {4,98}*784, {14,28}*784a, {14,28}*784b, {28,14}*784a, {28,14}*784c
15-fold covers : {30,14}*840, {10,42}*840, {6,70}*840, {2,210}*840
16-fold covers : {4,56}*896a, {8,56}*896a, {8,56}*896b, {8,28}*896a, {8,56}*896c, {8,56}*896d, {4,112}*896a, {4,112}*896b, {4,28}*896, {4,56}*896b, {8,28}*896b, {16,28}*896a, {16,28}*896b, {2,224}*896, {32,14}*896
17-fold covers : {34,14}*952, {2,238}*952
18-fold covers : {36,14}*1008, {18,28}*1008a, {2,252}*1008, {4,126}*1008a, {6,84}*1008a, {12,42}*1008a, {12,42}*1008b, {6,84}*1008b, {6,84}*1008c, {12,42}*1008c, {4,28}*1008, {4,42}*1008, {6,28}*1008
19-fold covers : {38,14}*1064, {2,266}*1064
20-fold covers : {40,14}*1120, {10,56}*1120, {20,28}*1120, {4,140}*1120, {2,280}*1120, {8,70}*1120
21-fold covers : {6,98}*1176, {2,294}*1176, {42,14}*1176a, {14,42}*1176b, {14,42}*1176c, {42,14}*1176b
22-fold covers : {22,28}*1232, {44,14}*1232, {2,308}*1232, {4,154}*1232
23-fold covers : {46,14}*1288, {2,322}*1288
24-fold covers : {48,14}*1344, {6,112}*1344, {12,28}*1344a, {24,28}*1344a, {12,56}*1344a, {24,28}*1344b, {12,56}*1344b, {4,168}*1344a, {4,84}*1344a, {4,168}*1344b, {8,84}*1344a, {8,84}*1344b, {2,336}*1344, {16,42}*1344, {12,28}*1344b, {6,28}*1344e, {6,84}*1344a, {12,42}*1344a, {6,42}*1344, {6,56}*1344b, {6,56}*1344c, {6,84}*1344b, {12,28}*1344c, {12,42}*1344b, {4,84}*1344b, {4,42}*1344b, {4,84}*1344c, {8,42}*1344b, {8,42}*1344c
25-fold covers : {50,14}*1400, {2,350}*1400, {10,70}*1400a, {10,70}*1400b, {10,70}*1400c
26-fold covers : {26,28}*1456, {52,14}*1456, {2,364}*1456, {4,182}*1456
27-fold covers : {54,14}*1512, {2,378}*1512, {18,42}*1512a, {6,42}*1512a, {6,126}*1512a, {6,126}*1512b, {18,42}*1512b, {6,42}*1512b, {6,42}*1512c, {6,42}*1512d
28-fold covers : {4,196}*1568, {2,392}*1568, {8,98}*1568, {14,56}*1568a, {14,56}*1568b, {56,14}*1568a, {28,28}*1568a, {28,28}*1568b, {56,14}*1568c
29-fold covers : {58,14}*1624, {2,406}*1624
30-fold covers : {60,14}*1680, {30,28}*1680a, {20,42}*1680a, {10,84}*1680, {12,70}*1680, {6,140}*1680a, {2,420}*1680, {4,210}*1680a
31-fold covers : {62,14}*1736, {2,434}*1736
32-fold covers : {8,56}*1792a, {8,28}*1792a, {8,56}*1792b, {4,56}*1792a, {8,56}*1792c, {8,56}*1792d, {16,28}*1792a, {4,112}*1792a, {16,28}*1792b, {4,112}*1792b, {8,112}*1792a, {16,56}*1792a, {8,112}*1792b, {16,56}*1792b, {16,56}*1792c, {8,112}*1792c, {8,112}*1792d, {16,56}*1792d, {16,56}*1792e, {8,112}*1792e, {8,112}*1792f, {16,56}*1792f, {32,28}*1792a, {4,224}*1792a, {32,28}*1792b, {4,224}*1792b, {4,28}*1792, {4,56}*1792b, {8,28}*1792b, {8,28}*1792c, {8,56}*1792e, {4,56}*1792c, {4,56}*1792d, {8,28}*1792d, {8,56}*1792f, {8,56}*1792g, {8,56}*1792h, {64,14}*1792, {2,448}*1792
33-fold covers : {22,42}*1848, {66,14}*1848, {6,154}*1848, {2,462}*1848
34-fold covers : {34,28}*1904, {68,14}*1904, {2,476}*1904, {4,238}*1904
35-fold covers : {10,98}*1960, {2,490}*1960, {70,14}*1960a, {14,70}*1960b, {14,70}*1960c, {70,14}*1960b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,16);;
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*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(16)!(1,2);
s1 := Sym(16)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(16)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,16);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope