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Polytope of Type {4,2,9,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,9,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 5
Schlafli Type : {4,2,9,4}
Number of vertices, edges, etc : 4, 4, 18, 36, 8
Order of s0s1s2s3s4 : 36
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 : {4,2,9,4}*576, {2,2,9,4}*576
   3-fold quotients : {4,2,3,4}*384
   4-fold quotients : {4,2,9,2}*288, {2,2,9,4}*288
   6-fold quotients : {4,2,3,4}*192, {2,2,3,4}*192
   8-fold quotients : {2,2,9,2}*144
   12-fold quotients : {4,2,3,2}*96, {2,2,3,4}*96
   24-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 9,13)(10,15)(11,14)(12,16)(17,33)(18,35)(19,34)(20,36)(21,29)
(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40)(42,43)(45,49)(46,51)(47,50)
(48,52)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)(59,66)(60,68)(61,73)(62,75)
(63,74)(64,76);;
s3 := ( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,21)(14,22)
(15,24)(16,23)(29,33)(30,34)(31,36)(32,35)(39,40)(41,53)(42,54)(43,56)(44,55)
(45,61)(46,62)(47,64)(48,63)(49,57)(50,58)(51,60)(52,59)(65,69)(66,70)(67,72)
(68,71)(75,76);;
s4 := ( 5,44)( 6,43)( 7,42)( 8,41)( 9,48)(10,47)(11,46)(12,45)(13,52)(14,51)
(15,50)(16,49)(17,56)(18,55)(19,54)(20,53)(21,60)(22,59)(23,58)(24,57)(25,64)
(26,63)(27,62)(28,61)(29,68)(30,67)(31,66)(32,65)(33,72)(34,71)(35,70)(36,69)
(37,76)(38,75)(39,74)(40,73);;
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*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*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(76)!(2,3);
s1 := Sym(76)!(1,2)(3,4);
s2 := Sym(76)!( 6, 7)( 9,13)(10,15)(11,14)(12,16)(17,33)(18,35)(19,34)(20,36)
(21,29)(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40)(42,43)(45,49)(46,51)
(47,50)(48,52)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)(59,66)(60,68)(61,73)
(62,75)(63,74)(64,76);
s3 := Sym(76)!( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,21)
(14,22)(15,24)(16,23)(29,33)(30,34)(31,36)(32,35)(39,40)(41,53)(42,54)(43,56)
(44,55)(45,61)(46,62)(47,64)(48,63)(49,57)(50,58)(51,60)(52,59)(65,69)(66,70)
(67,72)(68,71)(75,76);
s4 := Sym(76)!( 5,44)( 6,43)( 7,42)( 8,41)( 9,48)(10,47)(11,46)(12,45)(13,52)
(14,51)(15,50)(16,49)(17,56)(18,55)(19,54)(20,53)(21,60)(22,59)(23,58)(24,57)
(25,64)(26,63)(27,62)(28,61)(29,68)(30,67)(31,66)(32,65)(33,72)(34,71)(35,70)
(36,69)(37,76)(38,75)(39,74)(40,73);
poly := sub<Sym(76)|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*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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