Polytope of Type {2,4,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,38}*608
if this polytope has a name.
Group : SmallGroup(608,177)
Rank : 4
Schlafli Type : {2,4,38}
Number of vertices, edges, etc : 2, 4, 76, 38
Order of s₀s₁s₂s₃ : 76
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,38,2} of size 1216
Vertex Figure Of :
   {2,2,4,38} of size 1216
   {3,2,4,38} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,38}*304
   4-fold quotients : {2,2,19}*152
   19-fold quotients : {2,4,2}*32
   38-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,38}*1216, {2,4,76}*1216, {2,8,38}*1216
   3-fold covers : {2,12,38}*1824, {6,4,38}*1824, {2,4,114}*1824a
Permutation Representation (GAP) :

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