Polytope of Type {4,6,20,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,20,2}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240408)
Rank : 5
Schlafli Type : {4,6,20,2}
Number of vertices, edges, etc : 4, 12, 60, 20, 2
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   5-fold quotients : {4,6,4,2}*384e
   10-fold quotients : {4,3,4,2}*192
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)(17,25)(18,26)
(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)(37,45)
(38,46)(39,47)(40,48)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64)
(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(18,19)(21,25)(22,27)(23,26)
(24,28)(30,31)(34,35)(37,41)(38,43)(39,42)(40,44)(46,47)(50,51)(53,57)(54,59)
(55,58)(56,60)(62,63)(66,67)(69,73)(70,75)(71,74)(72,76)(78,79);;
s2 := ( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12)(17,65)(18,66)(19,68)(20,67)
(21,77)(22,78)(23,80)(24,79)(25,73)(26,74)(27,76)(28,75)(29,69)(30,70)(31,72)
(32,71)(33,49)(34,50)(35,52)(36,51)(37,61)(38,62)(39,64)(40,63)(41,57)(42,58)
(43,60)(44,59)(45,53)(46,54)(47,56)(48,55);;
s3 := ( 1,20)( 2,19)( 3,18)( 4,17)( 5,24)( 6,23)( 7,22)( 8,21)( 9,28)(10,27)
(11,26)(12,25)(13,32)(14,31)(15,30)(16,29)(33,68)(34,67)(35,66)(36,65)(37,72)
(38,71)(39,70)(40,69)(41,76)(42,75)(43,74)(44,73)(45,80)(46,79)(47,78)(48,77)
(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63);;
s4 := (81,82);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(82)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)
(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)
(37,45)(38,46)(39,47)(40,48)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)
(56,64)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80);
s1 := Sym(82)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(18,19)(21,25)(22,27)
(23,26)(24,28)(30,31)(34,35)(37,41)(38,43)(39,42)(40,44)(46,47)(50,51)(53,57)
(54,59)(55,58)(56,60)(62,63)(66,67)(69,73)(70,75)(71,74)(72,76)(78,79);
s2 := Sym(82)!( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12)(17,65)(18,66)(19,68)
(20,67)(21,77)(22,78)(23,80)(24,79)(25,73)(26,74)(27,76)(28,75)(29,69)(30,70)
(31,72)(32,71)(33,49)(34,50)(35,52)(36,51)(37,61)(38,62)(39,64)(40,63)(41,57)
(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55);
s3 := Sym(82)!( 1,20)( 2,19)( 3,18)( 4,17)( 5,24)( 6,23)( 7,22)( 8,21)( 9,28)
(10,27)(11,26)(12,25)(13,32)(14,31)(15,30)(16,29)(33,68)(34,67)(35,66)(36,65)
(37,72)(38,71)(39,70)(40,69)(41,76)(42,75)(43,74)(44,73)(45,80)(46,79)(47,78)
(48,77)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63);
s4 := Sym(82)!(81,82);
poly := sub<Sym(82)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2 >;

to this polytope