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Polytope of Type {4,2,4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,4,18}*1152c
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 5
Schlafli Type : {4,2,4,18}
Number of vertices, edges, etc : 4, 4, 4, 36, 18
Order of s0s1s2s3s4 : 36
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {4,2,4,9}*576, {2,2,4,18}*576c
   3-fold quotients : {4,2,4,6}*384b
   4-fold quotients : {2,2,4,9}*288
   6-fold quotients : {4,2,4,3}*192, {2,2,4,6}*192b
   12-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)(12,47)(13,50)(14,49)
(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)(23,60)(24,59)(25,62)
(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)(34,69)(35,72)(36,71)
(37,74)(38,73)(39,76)(40,75);;
s3 := ( 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);;
s4 := ( 5,53)( 6,54)( 7,56)( 8,55)( 9,61)(10,62)(11,64)(12,63)(13,57)(14,58)
(15,60)(16,59)(17,41)(18,42)(19,44)(20,43)(21,49)(22,50)(23,52)(24,51)(25,45)
(26,46)(27,48)(28,47)(29,69)(30,70)(31,72)(32,71)(33,65)(34,66)(35,68)(36,67)
(37,73)(38,74)(39,76)(40,75);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s4*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(76)!(2,3);
s1 := Sym(76)!(1,2)(3,4);
s2 := Sym(76)!( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)(12,47)(13,50)
(14,49)(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)(23,60)(24,59)
(25,62)(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)(34,69)(35,72)
(36,71)(37,74)(38,73)(39,76)(40,75);
s3 := 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);
s4 := Sym(76)!( 5,53)( 6,54)( 7,56)( 8,55)( 9,61)(10,62)(11,64)(12,63)(13,57)
(14,58)(15,60)(16,59)(17,41)(18,42)(19,44)(20,43)(21,49)(22,50)(23,52)(24,51)
(25,45)(26,46)(27,48)(28,47)(29,69)(30,70)(31,72)(32,71)(33,65)(34,66)(35,68)
(36,67)(37,73)(38,74)(39,76)(40,75);
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s4*s2*s3*s2 >; 
 

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