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Polytope of Type {2,2,8,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,18}*1152
if this polytope has a name.
Group : SmallGroup(1152,152539)
Rank : 5
Schlafli Type : {2,2,8,18}
Number of vertices, edges, etc : 2, 2, 8, 72, 18
Order of s0s1s2s3s4 : 72
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 : {2,2,4,18}*576a
   3-fold quotients : {2,2,8,6}*384
   4-fold quotients : {2,2,2,18}*288
   6-fold quotients : {2,2,4,6}*192a
   8-fold quotients : {2,2,2,9}*144
   9-fold quotients : {2,2,8,2}*128
   12-fold quotients : {2,2,2,6}*96
   18-fold quotients : {2,2,4,2}*64
   24-fold quotients : {2,2,2,3}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(41,59)
(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)
(53,71)(54,72)(55,73)(56,74)(57,75)(58,76);;
s3 := ( 5,41)( 6,43)( 7,42)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)(14,50)
(15,52)(16,51)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,68)(24,70)(25,69)
(26,75)(27,74)(28,76)(29,72)(30,71)(31,73)(32,59)(33,61)(34,60)(35,66)(36,65)
(37,67)(38,63)(39,62)(40,64);;
s4 := ( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,26)(24,28)
(25,27)(29,30)(32,35)(33,37)(34,36)(38,39)(41,44)(42,46)(43,45)(47,48)(50,53)
(51,55)(52,54)(56,57)(59,62)(60,64)(61,63)(65,66)(68,71)(69,73)(70,72)
(74,75);;
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*s1*s0*s1, 
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)
(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)
(52,70)(53,71)(54,72)(55,73)(56,74)(57,75)(58,76);
s3 := Sym(76)!( 5,41)( 6,43)( 7,42)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)
(14,50)(15,52)(16,51)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,68)(24,70)
(25,69)(26,75)(27,74)(28,76)(29,72)(30,71)(31,73)(32,59)(33,61)(34,60)(35,66)
(36,65)(37,67)(38,63)(39,62)(40,64);
s4 := Sym(76)!( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,26)
(24,28)(25,27)(29,30)(32,35)(33,37)(34,36)(38,39)(41,44)(42,46)(43,45)(47,48)
(50,53)(51,55)(52,54)(56,57)(59,62)(60,64)(61,63)(65,66)(68,71)(69,73)(70,72)
(74,75);
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*s1*s0*s1, 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, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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