Polytope of Type {2,2,38,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,38,4}*1216
if this polytope has a name.
Group : SmallGroup(1216,1369)
Rank : 5
Schlafli Type : {2,2,38,4}
Number of vertices, edges, etc : 2, 2, 38, 76, 4
Order of s₀s₁s₂s₃s₄ : 76
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,2,38,2}*608
   4-fold quotients : {2,2,19,2}*304
   19-fold quotients : {2,2,2,4}*64
   38-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(25,42)
(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(44,61)(45,60)(46,59)
(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)(63,80)(64,79)(65,78)(66,77)(67,76)
(68,75)(69,74)(70,73)(71,72);;
s3 := ( 5, 6)( 7,23)( 8,22)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(24,25)
(26,42)(27,41)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)(43,63)(44,62)(45,80)
(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)(55,70)(56,69)
(57,68)(58,67)(59,66)(60,65)(61,64);;
s4 := ( 5,43)( 6,44)( 7,45)( 8,46)( 9,47)(10,48)(11,49)(12,50)(13,51)(14,52)
(15,53)(16,54)(17,55)(18,56)(19,57)(20,58)(21,59)(22,60)(23,61)(24,62)(25,63)
(26,64)(27,65)(28,66)(29,67)(30,68)(31,69)(32,70)(33,71)(34,72)(35,73)(36,74)
(37,75)(38,76)(39,77)(40,78)(41,79)(42,80);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!(1,2);
s1 := Sym(80)!(3,4);
s2 := Sym(80)!( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)(13,16)(14,15)
(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(44,61)(45,60)
(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)(63,80)(64,79)(65,78)(66,77)
(67,76)(68,75)(69,74)(70,73)(71,72);
s3 := Sym(80)!( 5, 6)( 7,23)( 8,22)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)
(24,25)(26,42)(27,41)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)(43,63)(44,62)
(45,80)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)(55,70)
(56,69)(57,68)(58,67)(59,66)(60,65)(61,64);
s4 := Sym(80)!( 5,43)( 6,44)( 7,45)( 8,46)( 9,47)(10,48)(11,49)(12,50)(13,51)
(14,52)(15,53)(16,54)(17,55)(18,56)(19,57)(20,58)(21,59)(22,60)(23,61)(24,62)
(25,63)(26,64)(27,65)(28,66)(29,67)(30,68)(31,69)(32,70)(33,71)(34,72)(35,73)
(36,74)(37,75)(38,76)(39,77)(40,78)(41,79)(42,80);
poly := sub<Sym(80)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope