Polytope of Type {6,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,238598)
Rank : 4
Schlafli Type : {6,20,4}
Number of vertices, edges, etc : 6, 120, 80, 8
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {6,20,2}*480b
   5-fold quotients : {6,4,4}*384c
   10-fold quotients : {3,4,4}*192a
   20-fold quotients : {6,4,2}*96b
   40-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)
(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(55,56)(57,61)
(58,62)(59,64)(60,63)(67,68)(71,72)(73,77)(74,78)(75,80)(76,79);;
s1 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(17,65)(18,68)(19,67)(20,66)
(21,77)(22,80)(23,79)(24,78)(25,73)(26,76)(27,75)(28,74)(29,69)(30,72)(31,71)
(32,70)(33,49)(34,52)(35,51)(36,50)(37,61)(38,64)(39,63)(40,62)(41,57)(42,60)
(43,59)(44,58)(45,53)(46,56)(47,55)(48,54);;
s2 := ( 1,21)( 2,22)( 3,23)( 4,24)( 5,17)( 6,18)( 7,19)( 8,20)( 9,29)(10,30)
(11,31)(12,32)(13,25)(14,26)(15,27)(16,28)(33,69)(34,70)(35,71)(36,72)(37,65)
(38,66)(39,67)(40,68)(41,77)(42,78)(43,79)(44,80)(45,73)(46,74)(47,75)(48,76)
(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64);;
s3 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(21,22)(23,24)(25,27)(26,28)
(29,32)(30,31)(37,38)(39,40)(41,43)(42,44)(45,48)(46,47)(53,54)(55,56)(57,59)
(58,60)(61,64)(62,63)(69,70)(71,72)(73,75)(74,76)(77,80)(78,79);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)
(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(55,56)
(57,61)(58,62)(59,64)(60,63)(67,68)(71,72)(73,77)(74,78)(75,80)(76,79);
s1 := Sym(80)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(17,65)(18,68)(19,67)
(20,66)(21,77)(22,80)(23,79)(24,78)(25,73)(26,76)(27,75)(28,74)(29,69)(30,72)
(31,71)(32,70)(33,49)(34,52)(35,51)(36,50)(37,61)(38,64)(39,63)(40,62)(41,57)
(42,60)(43,59)(44,58)(45,53)(46,56)(47,55)(48,54);
s2 := Sym(80)!( 1,21)( 2,22)( 3,23)( 4,24)( 5,17)( 6,18)( 7,19)( 8,20)( 9,29)
(10,30)(11,31)(12,32)(13,25)(14,26)(15,27)(16,28)(33,69)(34,70)(35,71)(36,72)
(37,65)(38,66)(39,67)(40,68)(41,77)(42,78)(43,79)(44,80)(45,73)(46,74)(47,75)
(48,76)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64);
s3 := Sym(80)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(21,22)(23,24)(25,27)
(26,28)(29,32)(30,31)(37,38)(39,40)(41,43)(42,44)(45,48)(46,47)(53,54)(55,56)
(57,59)(58,60)(61,64)(62,63)(69,70)(71,72)(73,75)(74,76)(77,80)(78,79);
poly := sub<Sym(80)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1 >;

References : None.
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