Polytope of Type {2,38,4}

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

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

Permutation Representation (Magma) :

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

to this polytope