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Polytope of Type {6,30,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,30,2}*720b
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 4
Schlafli Type : {6,30,2}
Number of vertices, edges, etc : 6, 90, 30, 2
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,30,2,2} of size 1440
Vertex Figure Of :
   {2,6,30,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,10,2}*240, {2,30,2}*240
   5-fold quotients : {6,6,2}*144a
   6-fold quotients : {2,15,2}*120
   9-fold quotients : {2,10,2}*80
   15-fold quotients : {2,6,2}*48, {6,2,2}*48
   18-fold quotients : {2,5,2}*40
   30-fold quotients : {2,3,2}*24, {3,2,2}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,30,2}*1440b, {6,60,2}*1440b, {6,30,4}*1440b
Permutation Representation (GAP) :
s0 := (16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)
(26,41)(27,42)(28,43)(29,44)(30,45)(61,76)(62,77)(63,78)(64,79)(65,80)(66,81)
(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90);;
s1 := ( 1,16)( 2,20)( 3,19)( 4,18)( 5,17)( 6,26)( 7,30)( 8,29)( 9,28)(10,27)
(11,21)(12,25)(13,24)(14,23)(15,22)(32,35)(33,34)(36,41)(37,45)(38,44)(39,43)
(40,42)(46,61)(47,65)(48,64)(49,63)(50,62)(51,71)(52,75)(53,74)(54,73)(55,72)
(56,66)(57,70)(58,69)(59,68)(60,67)(77,80)(78,79)(81,86)(82,90)(83,89)(84,88)
(85,87);;
s2 := ( 1,52)( 2,51)( 3,55)( 4,54)( 5,53)( 6,47)( 7,46)( 8,50)( 9,49)(10,48)
(11,57)(12,56)(13,60)(14,59)(15,58)(16,67)(17,66)(18,70)(19,69)(20,68)(21,62)
(22,61)(23,65)(24,64)(25,63)(26,72)(27,71)(28,75)(29,74)(30,73)(31,82)(32,81)
(33,85)(34,84)(35,83)(36,77)(37,76)(38,80)(39,79)(40,78)(41,87)(42,86)(43,90)
(44,89)(45,88);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(92)!(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)
(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(61,76)(62,77)(63,78)(64,79)(65,80)
(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90);
s1 := Sym(92)!( 1,16)( 2,20)( 3,19)( 4,18)( 5,17)( 6,26)( 7,30)( 8,29)( 9,28)
(10,27)(11,21)(12,25)(13,24)(14,23)(15,22)(32,35)(33,34)(36,41)(37,45)(38,44)
(39,43)(40,42)(46,61)(47,65)(48,64)(49,63)(50,62)(51,71)(52,75)(53,74)(54,73)
(55,72)(56,66)(57,70)(58,69)(59,68)(60,67)(77,80)(78,79)(81,86)(82,90)(83,89)
(84,88)(85,87);
s2 := Sym(92)!( 1,52)( 2,51)( 3,55)( 4,54)( 5,53)( 6,47)( 7,46)( 8,50)( 9,49)
(10,48)(11,57)(12,56)(13,60)(14,59)(15,58)(16,67)(17,66)(18,70)(19,69)(20,68)
(21,62)(22,61)(23,65)(24,64)(25,63)(26,72)(27,71)(28,75)(29,74)(30,73)(31,82)
(32,81)(33,85)(34,84)(35,83)(36,77)(37,76)(38,80)(39,79)(40,78)(41,87)(42,86)
(43,90)(44,89)(45,88);
s3 := Sym(92)!(91,92);
poly := sub<Sym(92)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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