# Polytope of Type {6,12,2}

Atlas Canonical Name : {6,12,2}*576b
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 4
Schlafli Type : {6,12,2}
Number of vertices, edges, etc : 12, 72, 24, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,12,2,2} of size 1152
{6,12,2,3} of size 1728
Vertex Figure Of :
{2,6,12,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,12,2}*288
3-fold quotients : {6,4,2}*192
4-fold quotients : {6,6,2}*144c
6-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
8-fold quotients : {3,6,2}*72
12-fold quotients : {3,4,2}*48, {6,2,2}*48
24-fold quotients : {3,2,2}*24
36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,12,2}*1152e, {12,12,2}*1152h, {6,24,2}*1152b, {6,24,2}*1152d, {6,12,4}*1152j, {6,12,2}*1152f
3-fold covers : {18,12,2}*1728b, {6,12,2}*1728a, {6,12,6}*1728l, {6,12,2}*1728c
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,25)(14,27)(15,26)(16,28)(17,33)
(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(38,39)(41,45)(42,47)(43,46)
(44,48)(49,61)(50,63)(51,62)(52,64)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)
(59,66)(60,68);;
s1 := ( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)
(11,60)(12,59)(13,41)(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)(21,45)
(22,46)(23,48)(24,47)(25,65)(26,66)(27,68)(28,67)(29,61)(30,62)(31,64)(32,63)
(33,69)(34,70)(35,72)(36,71);;
s2 := ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9)(13,16)(14,15)(17,24)(18,23)
(19,22)(20,21)(25,28)(26,27)(29,36)(30,35)(31,34)(32,33)(37,40)(38,39)(41,48)
(42,47)(43,46)(44,45)(49,52)(50,51)(53,60)(54,59)(55,58)(56,57)(61,64)(62,63)
(65,72)(66,71)(67,70)(68,69);;
s3 := (73,74);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(74)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,25)(14,27)(15,26)(16,28)
(17,33)(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(38,39)(41,45)(42,47)
(43,46)(44,48)(49,61)(50,63)(51,62)(52,64)(53,69)(54,71)(55,70)(56,72)(57,65)
(58,67)(59,66)(60,68);
s1 := Sym(74)!( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)
(10,58)(11,60)(12,59)(13,41)(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)
(21,45)(22,46)(23,48)(24,47)(25,65)(26,66)(27,68)(28,67)(29,61)(30,62)(31,64)
(32,63)(33,69)(34,70)(35,72)(36,71);
s2 := Sym(74)!( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9)(13,16)(14,15)(17,24)
(18,23)(19,22)(20,21)(25,28)(26,27)(29,36)(30,35)(31,34)(32,33)(37,40)(38,39)
(41,48)(42,47)(43,46)(44,45)(49,52)(50,51)(53,60)(54,59)(55,58)(56,57)(61,64)
(62,63)(65,72)(66,71)(67,70)(68,69);
s3 := Sym(74)!(73,74);
poly := sub<Sym(74)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >;

```

to this polytope