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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,38}*1824
if this polytope has a name.
Group : SmallGroup(1824,1141)
Rank : 5
Schlafli Type : {3,2,4,38}
Number of vertices, edges, etc : 3, 3, 4, 76, 38
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 : {3,2,2,38}*912
   4-fold quotients : {3,2,2,19}*456
   19-fold quotients : {3,2,4,2}*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 := (42,61)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)
(52,71)(53,72)(54,73)(55,74)(56,75)(57,76)(58,77)(59,78)(60,79);;
s3 := ( 4,42)( 5,60)( 6,59)( 7,58)( 8,57)( 9,56)(10,55)(11,54)(12,53)(13,52)
(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,61)(24,79)
(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)
(36,67)(37,66)(38,65)(39,64)(40,63)(41,62);;
s4 := ( 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)(42,43)(44,60)(45,59)
(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(61,62)(63,79)(64,78)(65,77)(66,76)
(67,75)(68,74)(69,73)(70,72);;
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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope