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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,18,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,134249)
Rank : 5
Schlafli Type : {4,4,18,2}
Number of vertices, edges, etc : 4, 8, 36, 18, 2
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 : {2,4,18,2}*576a, {4,2,18,2}*576
   3-fold quotients : {4,4,6,2}*384
   4-fold quotients : {4,2,9,2}*288, {2,2,18,2}*288
   6-fold quotients : {2,4,6,2}*192a, {4,2,6,2}*192
   8-fold quotients : {2,2,9,2}*144
   9-fold quotients : {4,4,2,2}*128
   12-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   18-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   24-fold quotients : {2,2,3,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (37,46)(38,47)(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(55,64)
(56,65)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72);;
s1 := ( 1,37)( 2,38)( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)
(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)
(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)
(33,69)(34,70)(35,71)(36,72);;
s2 := ( 2, 3)( 4, 9)( 5, 8)( 6, 7)(11,12)(13,18)(14,17)(15,16)(20,21)(22,27)
(23,26)(24,25)(29,30)(31,36)(32,35)(33,34)(37,55)(38,57)(39,56)(40,63)(41,62)
(42,61)(43,60)(44,59)(45,58)(46,64)(47,66)(48,65)(49,72)(50,71)(51,70)(52,69)
(53,68)(54,67);;
s3 := ( 1, 4)( 2, 6)( 3, 5)( 7, 9)(10,13)(11,15)(12,14)(16,18)(19,22)(20,24)
(21,23)(25,27)(28,31)(29,33)(30,32)(34,36)(37,40)(38,42)(39,41)(43,45)(46,49)
(47,51)(48,50)(52,54)(55,58)(56,60)(57,59)(61,63)(64,67)(65,69)(66,68)
(70,72);;
s4 := (73,74);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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(74)!(37,46)(38,47)(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)
(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72);
s1 := Sym(74)!( 1,37)( 2,38)( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)
(10,46)(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)
(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)
(32,68)(33,69)(34,70)(35,71)(36,72);
s2 := Sym(74)!( 2, 3)( 4, 9)( 5, 8)( 6, 7)(11,12)(13,18)(14,17)(15,16)(20,21)
(22,27)(23,26)(24,25)(29,30)(31,36)(32,35)(33,34)(37,55)(38,57)(39,56)(40,63)
(41,62)(42,61)(43,60)(44,59)(45,58)(46,64)(47,66)(48,65)(49,72)(50,71)(51,70)
(52,69)(53,68)(54,67);
s3 := Sym(74)!( 1, 4)( 2, 6)( 3, 5)( 7, 9)(10,13)(11,15)(12,14)(16,18)(19,22)
(20,24)(21,23)(25,27)(28,31)(29,33)(30,32)(34,36)(37,40)(38,42)(39,41)(43,45)
(46,49)(47,51)(48,50)(52,54)(55,58)(56,60)(57,59)(61,63)(64,67)(65,69)(66,68)
(70,72);
s4 := Sym(74)!(73,74);
poly := sub<Sym(74)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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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