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# Polytope of Type {4,30}

Atlas Canonical Name : {4,30}*1200b
if this polytope has a name.
Group : SmallGroup(1200,961)
Rank : 3
Schlafli Type : {4,30}
Number of vertices, edges, etc : 20, 300, 150
Order of s0s1s2 : 12
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,10}*400
6-fold quotients : {4,10}*200
25-fold quotients : {4,6}*48a
50-fold quotients : {2,6}*24
75-fold quotients : {4,2}*16
100-fold quotients : {2,3}*12
150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 2,12)( 3,23)( 4, 9)( 5,20)( 6,21)( 8,18)(10,15)(11,16)(14,24)(17,22)
(27,37)(28,48)(29,34)(30,45)(31,46)(33,43)(35,40)(36,41)(39,49)(42,47)(52,62)
(53,73)(54,59)(55,70)(56,71)(58,68)(60,65)(61,66)(64,74)(67,72);;
s1 := ( 2, 9)( 3,12)( 4,20)( 5,23)( 6,13)( 7,16)( 8,24)(11,25)(15,17)(19,21)
(26,51)(27,59)(28,62)(29,70)(30,73)(31,63)(32,66)(33,74)(34,52)(35,60)(36,75)
(37,53)(38,56)(39,64)(40,67)(41,57)(42,65)(43,68)(44,71)(45,54)(46,69)(47,72)
(48,55)(49,58)(50,61);;
s2 := ( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,27)( 7,26)( 8,30)( 9,29)(10,28)
(11,47)(12,46)(13,50)(14,49)(15,48)(16,42)(17,41)(18,45)(19,44)(20,43)(21,37)
(22,36)(23,40)(24,39)(25,38)(51,57)(52,56)(53,60)(54,59)(55,58)(61,72)(62,71)
(63,75)(64,74)(65,73)(66,67)(68,70);;
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*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(75)!( 2,12)( 3,23)( 4, 9)( 5,20)( 6,21)( 8,18)(10,15)(11,16)(14,24)
(17,22)(27,37)(28,48)(29,34)(30,45)(31,46)(33,43)(35,40)(36,41)(39,49)(42,47)
(52,62)(53,73)(54,59)(55,70)(56,71)(58,68)(60,65)(61,66)(64,74)(67,72);
s1 := Sym(75)!( 2, 9)( 3,12)( 4,20)( 5,23)( 6,13)( 7,16)( 8,24)(11,25)(15,17)
(19,21)(26,51)(27,59)(28,62)(29,70)(30,73)(31,63)(32,66)(33,74)(34,52)(35,60)
(36,75)(37,53)(38,56)(39,64)(40,67)(41,57)(42,65)(43,68)(44,71)(45,54)(46,69)
(47,72)(48,55)(49,58)(50,61);
s2 := Sym(75)!( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,27)( 7,26)( 8,30)( 9,29)
(10,28)(11,47)(12,46)(13,50)(14,49)(15,48)(16,42)(17,41)(18,45)(19,44)(20,43)
(21,37)(22,36)(23,40)(24,39)(25,38)(51,57)(52,56)(53,60)(54,59)(55,58)(61,72)
(62,71)(63,75)(64,74)(65,73)(66,67)(68,70);
poly := sub<Sym(75)|s0,s1,s2>;

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

```
References : None.
to this polytope