Polytope of Type {2,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240977)
Rank : 4
Schlafli Type : {2,8,6}
Number of vertices, edges, etc : 2, 80, 240, 60
Order of s₀s₁s₂s₃ : 20
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 : {2,4,6}*960
   4-fold quotients : {2,4,6}*480a, {2,4,6}*480b, {2,4,6}*480c
   8-fold quotients : {2,4,6}*240
   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 := ( 3,12)( 4,63)( 5,72)( 6,15)( 7, 8)( 9,43)(10,34)(11,56)(13,41)(14,37)
(16,35)(17,44)(18,23)(19,39)(20,33)(21,40)(22,71)(24,52)(25,68)(26,74)(27,53)
(28,60)(29,47)(30,61)(31,50)(32,45)(36,49)(38,48)(42,64)(46,55)(51,57)(54,66)
(58,77)(59,79)(62,82)(65,75)(67,78)(69,81)(70,76)(73,80);;
s3 := ( 3,15)( 4,18)( 5,74)( 6,69)( 7,46)( 8,24)( 9,32)(10,76)(11,57)(12,82)
(13,43)(14,77)(16,28)(17,25)(19,75)(20,22)(21,38)(23,63)(26,51)(27,61)(29,45)
(30,62)(31,73)(33,66)(34,50)(35,60)(36,68)(37,70)(39,72)(40,64)(41,59)(42,52)
(44,49)(47,78)(48,55)(53,81)(54,71)(56,65)(58,80)(67,79);;
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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*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)!( 3,12)( 4,63)( 5,72)( 6,15)( 7, 8)( 9,43)(10,34)(11,56)(13,41)
(14,37)(16,35)(17,44)(18,23)(19,39)(20,33)(21,40)(22,71)(24,52)(25,68)(26,74)
(27,53)(28,60)(29,47)(30,61)(31,50)(32,45)(36,49)(38,48)(42,64)(46,55)(51,57)
(54,66)(58,77)(59,79)(62,82)(65,75)(67,78)(69,81)(70,76)(73,80);
s3 := Sym(82)!( 3,15)( 4,18)( 5,74)( 6,69)( 7,46)( 8,24)( 9,32)(10,76)(11,57)
(12,82)(13,43)(14,77)(16,28)(17,25)(19,75)(20,22)(21,38)(23,63)(26,51)(27,61)
(29,45)(30,62)(31,73)(33,66)(34,50)(35,60)(36,68)(37,70)(39,72)(40,64)(41,59)
(42,52)(44,49)(47,78)(48,55)(53,81)(54,71)(56,65)(58,80)(67,79);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2 >;

to this polytope