# Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238599)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 160, 480, 32
Order of s0s1s2 : 40
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {30,6}*480
5-fold quotients : {6,6}*384d
8-fold quotients : {15,6}*240
10-fold quotients : {6,3}*192
20-fold quotients : {6,6}*96
40-fold quotients : {3,6}*48, {6,3}*48
48-fold quotients : {10,2}*40
80-fold quotients : {3,3}*24
96-fold quotients : {5,2}*20
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(17,65)(18,66)(19,68)(20,67)
(21,70)(22,69)(23,71)(24,72)(25,77)(26,78)(27,80)(28,79)(29,73)(30,74)(31,76)
(32,75)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)(41,61)(42,62)
(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);;
s1 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,31)( 6,30)( 7,29)( 8,32)( 9,27)(10,26)
(11,25)(12,28)(13,23)(14,22)(15,21)(16,24)(33,65)(34,68)(35,67)(36,66)(37,79)
(38,78)(39,77)(40,80)(41,75)(42,74)(43,73)(44,76)(45,71)(46,70)(47,69)(48,72)
(50,52)(53,63)(54,62)(55,61)(56,64)(57,59);;
s2 := ( 1, 7)( 2, 8)( 3, 6)( 4, 5)(11,12)(15,16)(17,23)(18,24)(19,22)(20,21)
(27,28)(31,32)(33,39)(34,40)(35,38)(36,37)(43,44)(47,48)(49,55)(50,56)(51,54)
(52,53)(59,60)(63,64)(65,71)(66,72)(67,70)(68,69)(75,76)(79,80);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope