Polytope of Type {2,6,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,40}*1920a
if this polytope has a name.
Group : SmallGroup(1920,238293)
Rank : 4
Schlafli Type : {2,6,40}
Number of vertices, edges, etc : 2, 12, 240, 80
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   4-fold quotients : {2,6,20}*480b
   5-fold quotients : {2,6,8}*384a
   20-fold quotients : {2,6,4}*96b
   40-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope