Polytope of Type {2,40,6}

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

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

Permutation Representation (Magma) :

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

to this polytope