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Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1080a
if this polytope has a name.
Group : SmallGroup(1080,287)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 90, 270, 18
Order of s0s1s2 : 30
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {30,6}*360a
   5-fold quotients : {6,6}*216a
   9-fold quotients : {10,6}*120
   10-fold quotients : {6,3}*108
   15-fold quotients : {6,6}*72b
   27-fold quotients : {10,2}*40
   30-fold quotients : {6,3}*36
   45-fold quotients : {2,6}*24
   54-fold quotients : {5,2}*20
   90-fold quotients : {2,3}*12
   135-fold quotients : {2,2}*8
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)(17,18)(19,28)(20,30)
(21,29)(22,25)(23,27)(24,26)(32,33)(34,43)(35,45)(36,44)(37,40)(38,42)
(39,41);;
s1 := ( 1, 4)( 2, 5)( 3, 6)( 7,13)( 8,14)( 9,15)(16,36)(17,34)(18,35)(19,33)
(20,31)(21,32)(22,45)(23,43)(24,44)(25,42)(26,40)(27,41)(28,39)(29,37)
(30,38);;
s2 := ( 1,16)( 2,17)( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)(10,25)
(11,26)(12,27)(13,28)(14,29)(15,30);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(45)!( 2, 3)( 4,13)( 5,15)( 6,14)( 7,10)( 8,12)( 9,11)(17,18)(19,28)
(20,30)(21,29)(22,25)(23,27)(24,26)(32,33)(34,43)(35,45)(36,44)(37,40)(38,42)
(39,41);
s1 := Sym(45)!( 1, 4)( 2, 5)( 3, 6)( 7,13)( 8,14)( 9,15)(16,36)(17,34)(18,35)
(19,33)(20,31)(21,32)(22,45)(23,43)(24,44)(25,42)(26,40)(27,41)(28,39)(29,37)
(30,38);
s2 := Sym(45)!( 1,16)( 2,17)( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)
(10,25)(11,26)(12,27)(13,28)(14,29)(15,30);
poly := sub<Sym(45)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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