Polytope of Type {4,38,2}

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

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