Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240977)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 80, 240, 40
Order of s₀s₁s₂s₃ : 6
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 : {2,6,6}*960
   4-fold quotients : {2,6,6}*480a, {2,6,6}*480b, {2,6,6}*480c
   8-fold quotients : {2,6,6}*240
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope