Polytope of Type {2,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240977)
Rank : 4
Schlafli Type : {2,20,6}
Number of vertices, edges, etc : 2, 80, 240, 24
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   2-fold quotients : {2,10,6}*960b
   4-fold quotients : {2,5,6}*480a, {2,10,6}*480a, {2,10,6}*480b
   8-fold quotients : {2,5,6}*240a
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope