Polytope of Type {2,6,20}

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

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

Permutation Representation (Magma) :

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

to this polytope