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Polytope of Type {20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,238598)
Rank : 3
Schlafli Type : {20,6}
Number of vertices, edges, etc : 160, 480, 48
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
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 : {20,6}*480c
   5-fold quotients : {4,6}*384a
   8-fold quotients : {20,6}*240b
   10-fold quotients : {4,6}*192a
   16-fold quotients : {10,6}*120
   20-fold quotients : {4,6}*96
   40-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {5,2}*20
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,73)(18,74)
(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)
(30,70)(31,71)(32,72)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)
(41,49)(42,50)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56);;
s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,32)(10,31)
(11,29)(12,30)(13,27)(14,28)(15,26)(16,25)(33,65)(34,66)(35,68)(36,67)(37,70)
(38,69)(39,71)(40,72)(41,80)(42,79)(43,77)(44,78)(45,75)(46,76)(47,74)(48,73)
(51,52)(53,54)(57,64)(58,63)(59,61)(60,62);;
s2 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)(23,31)
(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44)(50,52)(53,61)(54,64)
(55,63)(56,62)(58,60)(66,68)(69,77)(70,80)(71,79)(72,78)(74,76);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(80)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,73)
(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)
(29,69)(30,70)(31,71)(32,72)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)
(40,64)(41,49)(42,50)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56);
s1 := Sym(80)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,32)
(10,31)(11,29)(12,30)(13,27)(14,28)(15,26)(16,25)(33,65)(34,66)(35,68)(36,67)
(37,70)(38,69)(39,71)(40,72)(41,80)(42,79)(43,77)(44,78)(45,75)(46,76)(47,74)
(48,73)(51,52)(53,54)(57,64)(58,63)(59,61)(60,62);
s2 := Sym(80)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)
(23,31)(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44)(50,52)(53,61)
(54,64)(55,63)(56,62)(58,60)(66,68)(69,77)(70,80)(71,79)(72,78)(74,76);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1 >; 
 
References : None.
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