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# Polytope of Type {6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20}*960b
if this polytope has a name.
Group : SmallGroup(960,10877)
Rank : 3
Schlafli Type : {6,20}
Number of vertices, edges, etc : 24, 240, 80
Order of s0s1s2 : 8
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,20,2} of size 1920
Vertex Figure Of :
{2,6,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,10}*480b
4-fold quotients : {6,5}*240a, {6,10}*240a, {6,10}*240b
8-fold quotients : {6,5}*120a
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,20}*1920h, {12,20}*1920j, {6,20}*1920c
Permutation Representation (GAP) :
```s0 := ( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)(12,64)
(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)(28,39)
(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)(51,69)
(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);;
s1 := ( 2,36)( 3,27)( 4,35)( 5,37)( 6,66)( 7,61)( 8,63)( 9,69)(10,46)(11,47)
(12,45)(13,43)(14,44)(15,64)(16,71)(18,48)(19,70)(21,54)(22,32)(23,73)(24,74)
(26,75)(28,38)(29,76)(30,40)(31,77)(33,39)(41,80)(42,78)(49,58)(50,57)(51,56)
(52,53)(55,79)(59,72)(60,67);;
s2 := ( 1,44)( 2,11)( 3,48)( 4,63)( 5,13)( 6,27)( 7,20)( 8,74)( 9,26)(10,42)
(12,31)(14,55)(15,36)(16,41)(17,38)(18,30)(19,23)(21,46)(22,43)(24,66)(25,71)
(28,57)(29,59)(32,72)(33,56)(34,49)(35,65)(37,45)(39,60)(40,50)(47,80)(51,52)
(53,61)(54,67)(58,78)(62,73)(64,75)(68,77)(69,79)(70,76);;
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*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(80)!( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)
(12,64)(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)
(28,39)(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)
(51,69)(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);
s1 := Sym(80)!( 2,36)( 3,27)( 4,35)( 5,37)( 6,66)( 7,61)( 8,63)( 9,69)(10,46)
(11,47)(12,45)(13,43)(14,44)(15,64)(16,71)(18,48)(19,70)(21,54)(22,32)(23,73)
(24,74)(26,75)(28,38)(29,76)(30,40)(31,77)(33,39)(41,80)(42,78)(49,58)(50,57)
(51,56)(52,53)(55,79)(59,72)(60,67);
s2 := Sym(80)!( 1,44)( 2,11)( 3,48)( 4,63)( 5,13)( 6,27)( 7,20)( 8,74)( 9,26)
(10,42)(12,31)(14,55)(15,36)(16,41)(17,38)(18,30)(19,23)(21,46)(22,43)(24,66)
(25,71)(28,57)(29,59)(32,72)(33,56)(34,49)(35,65)(37,45)(39,60)(40,50)(47,80)
(51,52)(53,61)(54,67)(58,78)(62,73)(64,75)(68,77)(69,79)(70,76);
poly := sub<Sym(80)|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*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope