Polytope of Type {20,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,4}*960c
if this polytope has a name.
Group : SmallGroup(960,11373)
Rank : 4
Schlafli Type : {20,6,4}
Number of vertices, edges, etc : 20, 60, 12, 4
Order of s₀s₁s₂s₃ : 15
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,6,4,2} of size 1920
Vertex Figure Of :
   {2,20,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {4,6,4}*192f
   10-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,6,4}*1920c, {20,6,4}*1920d
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)( 2,19)( 3,18)( 4,20)( 5,25)( 6,27)( 7,26)( 8,28)( 9,21)(10,23)
(11,22)(12,24)(13,29)(14,31)(15,30)(16,32)(33,65)(34,67)(35,66)(36,68)(37,73)
(38,75)(39,74)(40,76)(41,69)(42,71)(43,70)(44,72)(45,77)(46,79)(47,78)(48,80)
(50,51)(53,57)(54,59)(55,58)(56,60)(62,63);;
s2 := ( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12)(19,20)(21,29)(22,30)(23,32)
(24,31)(27,28)(35,36)(37,45)(38,46)(39,48)(40,47)(43,44)(51,52)(53,61)(54,62)
(55,64)(56,63)(59,60)(67,68)(69,77)(70,78)(71,80)(72,79)(75,76);;
s3 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)
(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)
(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)
(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(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, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 ];;
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)( 2,19)( 3,18)( 4,20)( 5,25)( 6,27)( 7,26)( 8,28)( 9,21)
(10,23)(11,22)(12,24)(13,29)(14,31)(15,30)(16,32)(33,65)(34,67)(35,66)(36,68)
(37,73)(38,75)(39,74)(40,76)(41,69)(42,71)(43,70)(44,72)(45,77)(46,79)(47,78)
(48,80)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63);
s2 := Sym(80)!( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12)(19,20)(21,29)(22,30)
(23,32)(24,31)(27,28)(35,36)(37,45)(38,46)(39,48)(40,47)(43,44)(51,52)(53,61)
(54,62)(55,64)(56,63)(59,60)(67,68)(69,77)(70,78)(71,80)(72,79)(75,76);
s3 := Sym(80)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)
(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)
(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)
(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(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, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 >;

References : None.
to this polytope