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# Polytope of Type {2,4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,14}*224
if this polytope has a name.
Group : SmallGroup(224,178)
Rank : 4
Schlafli Type : {2,4,14}
Number of vertices, edges, etc : 2, 4, 28, 14
Order of s0s1s2s3 : 28
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,14,2} of size 448
{2,4,14,4} of size 896
{2,4,14,6} of size 1344
{2,4,14,7} of size 1568
{2,4,14,8} of size 1792
Vertex Figure Of :
{2,2,4,14} of size 448
{3,2,4,14} of size 672
{4,2,4,14} of size 896
{5,2,4,14} of size 1120
{6,2,4,14} of size 1344
{7,2,4,14} of size 1568
{8,2,4,14} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,14}*112
4-fold quotients : {2,2,7}*56
7-fold quotients : {2,4,2}*32
14-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,28}*448, {4,4,14}*448, {2,8,14}*448
3-fold covers : {2,12,14}*672, {6,4,14}*672, {2,4,42}*672a
4-fold covers : {4,4,28}*896, {2,4,56}*896a, {2,4,28}*896, {2,4,56}*896b, {2,8,28}*896a, {2,8,28}*896b, {4,8,14}*896a, {8,4,14}*896a, {4,8,14}*896b, {8,4,14}*896b, {4,4,14}*896, {2,16,14}*896
5-fold covers : {2,20,14}*1120, {10,4,14}*1120, {2,4,70}*1120
6-fold covers : {4,12,14}*1344a, {12,4,14}*1344, {6,4,28}*1344, {2,24,14}*1344, {6,8,14}*1344, {2,12,28}*1344, {2,4,84}*1344a, {4,4,42}*1344, {2,8,42}*1344
7-fold covers : {2,4,98}*1568, {2,28,14}*1568a, {14,4,14}*1568, {2,28,14}*1568c
8-fold covers : {4,8,14}*1792a, {8,4,14}*1792a, {2,8,28}*1792a, {2,4,56}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {8,8,14}*1792c, {2,8,56}*1792a, {2,8,56}*1792b, {2,8,56}*1792c, {8,8,14}*1792d, {2,8,56}*1792d, {8,4,28}*1792a, {4,4,56}*1792a, {8,4,28}*1792b, {4,4,56}*1792b, {4,8,28}*1792a, {4,4,28}*1792a, {4,4,28}*1792b, {4,8,28}*1792b, {4,8,28}*1792c, {4,8,28}*1792d, {4,16,14}*1792a, {16,4,14}*1792a, {2,16,28}*1792a, {2,4,112}*1792a, {4,16,14}*1792b, {16,4,14}*1792b, {2,16,28}*1792b, {2,4,112}*1792b, {4,4,14}*1792, {4,8,14}*1792b, {8,4,14}*1792b, {2,4,28}*1792, {2,4,56}*1792b, {2,8,28}*1792b, {2,32,14}*1792
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 7)( 8,13)( 9,14)(15,21)(16,22)(23,27)(24,28);;
s2 := ( 3, 4)( 5, 9)( 6, 8)( 7,12)(10,16)(11,15)(13,20)(14,19)(17,24)(18,23)
(21,26)(22,25)(27,30)(28,29);;
s3 := ( 3, 5)( 4, 8)( 6,10)( 7,13)( 9,15)(11,17)(12,19)(14,21)(16,23)(20,25)
(22,27)(26,29);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(30)!(1,2);
s1 := Sym(30)!( 4, 7)( 8,13)( 9,14)(15,21)(16,22)(23,27)(24,28);
s2 := Sym(30)!( 3, 4)( 5, 9)( 6, 8)( 7,12)(10,16)(11,15)(13,20)(14,19)(17,24)
(18,23)(21,26)(22,25)(27,30)(28,29);
s3 := Sym(30)!( 3, 5)( 4, 8)( 6,10)( 7,13)( 9,15)(11,17)(12,19)(14,21)(16,23)
(20,25)(22,27)(26,29);
poly := sub<Sym(30)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope