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# Polytope of Type {2,12,12}

Atlas Canonical Name : {2,12,12}*576a
if this polytope has a name.
Group : SmallGroup(576,6953)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 12, 72, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,12,12,2} of size 1152
Vertex Figure Of :
{2,2,12,12} of size 1152
{3,2,12,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,12}*288a, {2,12,6}*288a
3-fold quotients : {2,4,12}*192a, {2,12,4}*192a
4-fold quotients : {2,6,6}*144a
6-fold quotients : {2,2,12}*96, {2,12,2}*96, {2,4,6}*96a, {2,6,4}*96a
9-fold quotients : {2,4,4}*64
12-fold quotients : {2,2,6}*48, {2,6,2}*48
18-fold quotients : {2,2,4}*32, {2,4,2}*32
24-fold quotients : {2,2,3}*24, {2,3,2}*24
36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,12}*1152b, {2,12,24}*1152a, {2,24,12}*1152a, {2,12,24}*1152d, {2,24,12}*1152d, {2,12,12}*1152a
3-fold covers : {2,12,36}*1728a, {2,36,12}*1728a, {2,12,12}*1728c, {6,12,12}*1728b, {6,12,12}*1728d, {2,12,12}*1728h
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)
(34,37)(35,38)(39,57)(40,58)(41,59)(42,63)(43,64)(44,65)(45,60)(46,61)(47,62)
(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)(55,70)(56,71);;
s2 := ( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)(12,51)
(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)(23,61)
(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)(34,68)
(35,67)(36,72)(37,74)(38,73);;
s3 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,49)(40,48)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)(47,56)
(57,67)(58,66)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*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,
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(74)!(1,2);
s1 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)
(33,36)(34,37)(35,38)(39,57)(40,58)(41,59)(42,63)(43,64)(44,65)(45,60)(46,61)
(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)(55,70)(56,71);
s2 := Sym(74)!( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)
(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)
(23,61)(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)
(34,68)(35,67)(36,72)(37,74)(38,73);
s3 := Sym(74)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)
(30,31)(33,34)(36,37)(39,49)(40,48)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)
(47,56)(57,67)(58,66)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*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,
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