Polytope of Type {4,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,38}*304
Also Known As : {4,38|2}. if this polytope has another name.
Group : SmallGroup(304,31)
Rank : 3
Schlafli Type : {4,38}
Number of vertices, edges, etc : 4, 76, 38
Order of s₀s₁s₂ : 76
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,38,2} of size 608
   {4,38,4} of size 1216
   {4,38,6} of size 1824
Vertex Figure Of :
   {2,4,38} of size 608
   {4,4,38} of size 1216
   {6,4,38} of size 1824
   {3,4,38} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,38}*152
   4-fold quotients : {2,19}*76
   19-fold quotients : {4,2}*16
   38-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,76}*608, {8,38}*608
   3-fold covers : {12,38}*912, {4,114}*912a
   4-fold covers : {8,76}*1216a, {4,152}*1216a, {8,76}*1216b, {4,152}*1216b, {4,76}*1216, {16,38}*1216
   5-fold covers : {20,38}*1520, {4,190}*1520
   6-fold covers : {24,38}*1824, {12,76}*1824, {4,228}*1824a, {8,114}*1824
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(76)!(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(76)!( 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(76)!( 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);
poly := sub<Sym(76)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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 >;

References : None.
to this polytope