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Polytope of Type {90,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {90,2,3}*1080
if this polytope has a name.
Group : SmallGroup(1080,335)
Rank : 4
Schlafli Type : {90,2,3}
Number of vertices, edges, etc : 90, 90, 3, 3
Order of s0s1s2s3 : 90
Order of s0s1s2s3s2s1 : 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 : {45,2,3}*540
   3-fold quotients : {30,2,3}*360
   5-fold quotients : {18,2,3}*216
   6-fold quotients : {15,2,3}*180
   9-fold quotients : {10,2,3}*120
   10-fold quotients : {9,2,3}*108
   15-fold quotients : {6,2,3}*72
   18-fold quotients : {5,2,3}*60
   30-fold quotients : {3,2,3}*36
   45-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4,13)( 5,15)( 6,14)( 7,10)( 8,12)( 9,11)(16,32)(17,31)(18,33)
(19,44)(20,43)(21,45)(22,41)(23,40)(24,42)(25,38)(26,37)(27,39)(28,35)(29,34)
(30,36)(47,48)(49,58)(50,60)(51,59)(52,55)(53,57)(54,56)(61,77)(62,76)(63,78)
(64,89)(65,88)(66,90)(67,86)(68,85)(69,87)(70,83)(71,82)(72,84)(73,80)(74,79)
(75,81);;
s1 := ( 1,64)( 2,66)( 3,65)( 4,61)( 5,63)( 6,62)( 7,73)( 8,75)( 9,74)(10,70)
(11,72)(12,71)(13,67)(14,69)(15,68)(16,49)(17,51)(18,50)(19,46)(20,48)(21,47)
(22,58)(23,60)(24,59)(25,55)(26,57)(27,56)(28,52)(29,54)(30,53)(31,80)(32,79)
(33,81)(34,77)(35,76)(36,78)(37,89)(38,88)(39,90)(40,86)(41,85)(42,87)(43,83)
(44,82)(45,84);;
s2 := (92,93);;
s3 := (91,92);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(93)!( 2, 3)( 4,13)( 5,15)( 6,14)( 7,10)( 8,12)( 9,11)(16,32)(17,31)
(18,33)(19,44)(20,43)(21,45)(22,41)(23,40)(24,42)(25,38)(26,37)(27,39)(28,35)
(29,34)(30,36)(47,48)(49,58)(50,60)(51,59)(52,55)(53,57)(54,56)(61,77)(62,76)
(63,78)(64,89)(65,88)(66,90)(67,86)(68,85)(69,87)(70,83)(71,82)(72,84)(73,80)
(74,79)(75,81);
s1 := Sym(93)!( 1,64)( 2,66)( 3,65)( 4,61)( 5,63)( 6,62)( 7,73)( 8,75)( 9,74)
(10,70)(11,72)(12,71)(13,67)(14,69)(15,68)(16,49)(17,51)(18,50)(19,46)(20,48)
(21,47)(22,58)(23,60)(24,59)(25,55)(26,57)(27,56)(28,52)(29,54)(30,53)(31,80)
(32,79)(33,81)(34,77)(35,76)(36,78)(37,89)(38,88)(39,90)(40,86)(41,85)(42,87)
(43,83)(44,82)(45,84);
s2 := Sym(93)!(92,93);
s3 := Sym(93)!(91,92);
poly := sub<Sym(93)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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