Polytope of Type {3,2,38,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,38,4}*1824
if this polytope has a name.
Group : SmallGroup(1824,1141)
Rank : 5
Schlafli Type : {3,2,38,4}
Number of vertices, edges, etc : 3, 3, 38, 76, 4
Order of s₀s₁s₂s₃s₄ : 228
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 : {3,2,38,2}*912
   4-fold quotients : {3,2,19,2}*456
   19-fold quotients : {3,2,2,4}*96
   38-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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