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Polytope of Type {6,15,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,15,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,238293)
Rank : 4
Schlafli Type : {6,15,2}
Number of vertices, edges, etc : 32, 240, 80, 2
Order of s0s1s2s3 : 40
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) :
   4-fold quotients : {6,15,2}*480
   5-fold quotients : {6,3,2}*384
   20-fold quotients : {6,3,2}*96
   40-fold quotients : {3,3,2}*48
   48-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(19,20)(21,26)(22,25)(23,27)
(24,28)(31,32)(35,36)(37,42)(38,41)(39,43)(40,44)(47,48)(51,52)(53,58)(54,57)
(55,59)(56,60)(63,64)(67,68)(69,74)(70,73)(71,75)(72,76)(79,80);;
s1 := ( 2, 3)( 5, 8)( 9,16)(10,14)(11,15)(12,13)(17,65)(18,67)(19,66)(20,68)
(21,72)(22,70)(23,71)(24,69)(25,80)(26,78)(27,79)(28,77)(29,76)(30,74)(31,75)
(32,73)(33,49)(34,51)(35,50)(36,52)(37,56)(38,54)(39,55)(40,53)(41,64)(42,62)
(43,63)(44,61)(45,60)(46,58)(47,59)(48,57);;
s2 := ( 1,29)( 2,30)( 3,32)( 4,31)( 5,22)( 6,21)( 7,23)( 8,24)( 9,26)(10,25)
(11,27)(12,28)(13,17)(14,18)(15,20)(16,19)(33,77)(34,78)(35,80)(36,79)(37,70)
(38,69)(39,71)(40,72)(41,74)(42,73)(43,75)(44,76)(45,65)(46,66)(47,68)(48,67)
(49,61)(50,62)(51,64)(52,63)(53,54)(57,58);;
s3 := (81,82);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(82)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(19,20)(21,26)(22,25)
(23,27)(24,28)(31,32)(35,36)(37,42)(38,41)(39,43)(40,44)(47,48)(51,52)(53,58)
(54,57)(55,59)(56,60)(63,64)(67,68)(69,74)(70,73)(71,75)(72,76)(79,80);
s1 := Sym(82)!( 2, 3)( 5, 8)( 9,16)(10,14)(11,15)(12,13)(17,65)(18,67)(19,66)
(20,68)(21,72)(22,70)(23,71)(24,69)(25,80)(26,78)(27,79)(28,77)(29,76)(30,74)
(31,75)(32,73)(33,49)(34,51)(35,50)(36,52)(37,56)(38,54)(39,55)(40,53)(41,64)
(42,62)(43,63)(44,61)(45,60)(46,58)(47,59)(48,57);
s2 := Sym(82)!( 1,29)( 2,30)( 3,32)( 4,31)( 5,22)( 6,21)( 7,23)( 8,24)( 9,26)
(10,25)(11,27)(12,28)(13,17)(14,18)(15,20)(16,19)(33,77)(34,78)(35,80)(36,79)
(37,70)(38,69)(39,71)(40,72)(41,74)(42,73)(43,75)(44,76)(45,65)(46,66)(47,68)
(48,67)(49,61)(50,62)(51,64)(52,63)(53,54)(57,58);
s3 := Sym(82)!(81,82);
poly := sub<Sym(82)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

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