# Polytope of Type {12,4,2,3}

Atlas Canonical Name : {12,4,2,3}*576b
if this polytope has a name.
Group : SmallGroup(576,8312)
Rank : 5
Schlafli Type : {12,4,2,3}
Number of vertices, edges, etc : 12, 24, 4, 3, 3
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,4,2,3,2} of size 1152
Vertex Figure Of :
{2,12,4,2,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,4,2,3}*288c
4-fold quotients : {3,4,2,3}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,4,2,3}*1152c, {24,4,2,3}*1152d, {12,4,2,3}*1152b, {12,4,2,6}*1152b
3-fold covers : {12,4,2,9}*1728b, {36,4,2,3}*1728b
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)
(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)
(42,45);;
s1 := ( 1, 8)( 2, 4)( 3,19)( 5, 9)( 6,43)( 7,11)(10,34)(12,20)(13,48)(14,42)
(15,26)(16,25)(17,29)(18,23)(21,44)(22,33)(24,38)(27,47)(28,39)(30,37)(31,36)
(32,41)(35,45)(40,46);;
s2 := ( 1,33)( 2,42)( 3,45)( 4,34)( 5,18)( 6,16)( 7,47)( 8,43)( 9,26)(10,29)
(11,44)(12,31)(13,24)(14,17)(15,32)(19,48)(20,39)(21,37)(22,25)(23,41)(27,30)
(28,40)(35,38)(36,46);;
s3 := (50,51);;
s4 := (49,50);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s0*s2*s1*s2*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(51)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)
(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)
(39,48)(42,45);
s1 := Sym(51)!( 1, 8)( 2, 4)( 3,19)( 5, 9)( 6,43)( 7,11)(10,34)(12,20)(13,48)
(14,42)(15,26)(16,25)(17,29)(18,23)(21,44)(22,33)(24,38)(27,47)(28,39)(30,37)
(31,36)(32,41)(35,45)(40,46);
s2 := Sym(51)!( 1,33)( 2,42)( 3,45)( 4,34)( 5,18)( 6,16)( 7,47)( 8,43)( 9,26)
(10,29)(11,44)(12,31)(13,24)(14,17)(15,32)(19,48)(20,39)(21,37)(22,25)(23,41)
(27,30)(28,40)(35,38)(36,46);
s3 := Sym(51)!(50,51);
s4 := Sym(51)!(49,50);
poly := sub<Sym(51)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*s1*s2*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