# Polytope of Type {12,10}

Atlas Canonical Name : {12,10}*600
if this polytope has a name.
Group : SmallGroup(600,170)
Rank : 3
Schlafli Type : {12,10}
Number of vertices, edges, etc : 30, 150, 25
Order of s0s1s2 : 12
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,10,2} of size 1200
Vertex Figure Of :
{2,12,10} of size 1200
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,10}*200
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,10}*1200c
3-fold covers : {36,10}*1800
Permutation Representation (GAP) :
```s0 := ( 2,12)( 3,23)( 4, 9)( 5,20)( 6,21)( 8,18)(10,15)(11,16)(14,24)(17,22)
(26,51)(27,62)(28,73)(29,59)(30,70)(31,71)(32,57)(33,68)(34,54)(35,65)(36,66)
(37,52)(38,63)(39,74)(40,60)(41,61)(42,72)(43,58)(44,69)(45,55)(46,56)(47,67)
(48,53)(49,64)(50,75);;
s1 := ( 1,26)( 2,34)( 3,37)( 4,45)( 5,48)( 6,38)( 7,41)( 8,49)( 9,27)(10,35)
(11,50)(12,28)(13,31)(14,39)(15,42)(16,32)(17,40)(18,43)(19,46)(20,29)(21,44)
(22,47)(23,30)(24,33)(25,36)(52,59)(53,62)(54,70)(55,73)(56,63)(57,66)(58,74)
(61,75)(65,67)(69,71);;
s2 := ( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,22)(12,21)(13,25)(14,24)(15,23)
(16,17)(18,20)(26,32)(27,31)(28,35)(29,34)(30,33)(36,47)(37,46)(38,50)(39,49)
(40,48)(41,42)(43,45)(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*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2 ];;
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)(26,51)(27,62)(28,73)(29,59)(30,70)(31,71)(32,57)(33,68)(34,54)(35,65)
(36,66)(37,52)(38,63)(39,74)(40,60)(41,61)(42,72)(43,58)(44,69)(45,55)(46,56)
(47,67)(48,53)(49,64)(50,75);
s1 := Sym(75)!( 1,26)( 2,34)( 3,37)( 4,45)( 5,48)( 6,38)( 7,41)( 8,49)( 9,27)
(10,35)(11,50)(12,28)(13,31)(14,39)(15,42)(16,32)(17,40)(18,43)(19,46)(20,29)
(21,44)(22,47)(23,30)(24,33)(25,36)(52,59)(53,62)(54,70)(55,73)(56,63)(57,66)
(58,74)(61,75)(65,67)(69,71);
s2 := Sym(75)!( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,22)(12,21)(13,25)(14,24)
(15,23)(16,17)(18,20)(26,32)(27,31)(28,35)(29,34)(30,33)(36,47)(37,46)(38,50)
(39,49)(40,48)(41,42)(43,45)(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*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2 >;

```
References : None.
to this polytope