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Polytope of Type {3,2,2,4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,4,18}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46115)
Rank : 6
Schlafli Type : {3,2,2,4,18}
Number of vertices, edges, etc : 3, 3, 2, 4, 36, 18
Order of s0s1s2s3s4s5 : 18
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {3,2,2,4,9}*864
   3-fold quotients : {3,2,2,4,6}*576c
   6-fold quotients : {3,2,2,4,3}*288
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)
(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)
(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)
(70,71)(72,73)(74,75)(76,77);;
s4 := ( 7, 8)(10,14)(11,16)(12,15)(13,17)(18,34)(19,36)(20,35)(21,37)(22,30)
(23,32)(24,31)(25,33)(26,38)(27,40)(28,39)(29,41)(43,44)(46,50)(47,52)(48,51)
(49,53)(54,70)(55,72)(56,71)(57,73)(58,66)(59,68)(60,67)(61,69)(62,74)(63,76)
(64,75)(65,77);;
s5 := ( 6,54)( 7,55)( 8,57)( 9,56)(10,62)(11,63)(12,65)(13,64)(14,58)(15,59)
(16,61)(17,60)(18,42)(19,43)(20,45)(21,44)(22,50)(23,51)(24,53)(25,52)(26,46)
(27,47)(28,49)(29,48)(30,70)(31,71)(32,73)(33,72)(34,66)(35,67)(36,69)(37,68)
(38,74)(39,75)(40,77)(41,76);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(77)!(2,3);
s1 := Sym(77)!(1,2);
s2 := Sym(77)!(4,5);
s3 := Sym(77)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)
(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)
(68,69)(70,71)(72,73)(74,75)(76,77);
s4 := Sym(77)!( 7, 8)(10,14)(11,16)(12,15)(13,17)(18,34)(19,36)(20,35)(21,37)
(22,30)(23,32)(24,31)(25,33)(26,38)(27,40)(28,39)(29,41)(43,44)(46,50)(47,52)
(48,51)(49,53)(54,70)(55,72)(56,71)(57,73)(58,66)(59,68)(60,67)(61,69)(62,74)
(63,76)(64,75)(65,77);
s5 := Sym(77)!( 6,54)( 7,55)( 8,57)( 9,56)(10,62)(11,63)(12,65)(13,64)(14,58)
(15,59)(16,61)(17,60)(18,42)(19,43)(20,45)(21,44)(22,50)(23,51)(24,53)(25,52)
(26,46)(27,47)(28,49)(29,48)(30,70)(31,71)(32,73)(33,72)(34,66)(35,67)(36,69)
(37,68)(38,74)(39,75)(40,77)(41,76);
poly := sub<Sym(77)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

to this polytope