# Polytope of Type {30,6}

Atlas Canonical Name : {30,6}*900
if this polytope has a name.
Group : SmallGroup(900,95)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 75, 225, 15
Order of s0s1s2 : 3
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{30,6,2} of size 1800
Vertex Figure Of :
{2,30,6} of size 1800
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {10,6}*300
Covers (Minimal Covers in Boldface) :
2-fold covers : {30,6}*1800d
Permutation Representation (GAP) :
```s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)
(14,18)(15,17)(26,51)(27,55)(28,54)(29,53)(30,52)(31,71)(32,75)(33,74)(34,73)
(35,72)(36,66)(37,70)(38,69)(39,68)(40,67)(41,61)(42,65)(43,64)(44,63)(45,62)
(46,56)(47,60)(48,59)(49,58)(50,57);;
s1 := ( 1,27)( 2,26)( 3,30)( 4,29)( 5,28)( 6,35)( 7,34)( 8,33)( 9,32)(10,31)
(11,38)(12,37)(13,36)(14,40)(15,39)(16,41)(17,45)(18,44)(19,43)(20,42)(21,49)
(22,48)(23,47)(24,46)(25,50)(51,52)(53,55)(56,60)(57,59)(61,63)(64,65)(67,70)
(68,69)(71,74)(72,73);;
s2 := ( 2,24)( 3,17)( 4,15)( 5, 8)( 6,14)( 9,23)(10,16)(11,22)(12,20)(18,21)
(27,49)(28,42)(29,40)(30,33)(31,39)(34,48)(35,41)(36,47)(37,45)(43,46)(52,74)
(53,67)(54,65)(55,58)(56,64)(59,73)(60,66)(61,72)(62,70)(68,71);;
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*s2*s0*s1*s2*s0*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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(75)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)
(13,19)(14,18)(15,17)(26,51)(27,55)(28,54)(29,53)(30,52)(31,71)(32,75)(33,74)
(34,73)(35,72)(36,66)(37,70)(38,69)(39,68)(40,67)(41,61)(42,65)(43,64)(44,63)
(45,62)(46,56)(47,60)(48,59)(49,58)(50,57);
s1 := Sym(75)!( 1,27)( 2,26)( 3,30)( 4,29)( 5,28)( 6,35)( 7,34)( 8,33)( 9,32)
(10,31)(11,38)(12,37)(13,36)(14,40)(15,39)(16,41)(17,45)(18,44)(19,43)(20,42)
(21,49)(22,48)(23,47)(24,46)(25,50)(51,52)(53,55)(56,60)(57,59)(61,63)(64,65)
(67,70)(68,69)(71,74)(72,73);
s2 := Sym(75)!( 2,24)( 3,17)( 4,15)( 5, 8)( 6,14)( 9,23)(10,16)(11,22)(12,20)
(18,21)(27,49)(28,42)(29,40)(30,33)(31,39)(34,48)(35,41)(36,47)(37,45)(43,46)
(52,74)(53,67)(54,65)(55,58)(56,64)(59,73)(60,66)(61,72)(62,70)(68,71);
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*s2*s0*s1*s2*s0*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope