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Polytope of Type {20,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,2}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240977)
Rank : 4
Schlafli Type : {20,6,2}
Number of vertices, edges, etc : 80, 240, 24, 2
Order of s0s1s2s3 : 8
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 : {10,6,2}*960b
   4-fold quotients : {5,6,2}*480a, {10,6,2}*480a, {10,6,2}*480b
   8-fold quotients : {5,6,2}*240a
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2,26)( 3,75)( 4,80)( 5,41)( 6,70)( 7,68)( 8,43)( 9,19)(10,13)(11,12)
(15,64)(17,44)(18,47)(21,33)(22,39)(23,42)(24,78)(27,36)(28,79)(29,55)(30,53)
(31,52)(32,54)(35,37)(38,76)(40,77)(45,48)(46,63)(49,62)(50,72)(51,59)(56,57)
(60,67)(65,71)(66,69)(73,74);;
s1 := ( 1, 6)( 2,13)( 3,70)( 4,61)( 5,10)( 7,54)( 8,32)( 9,41)(11,55)(12,42)
(14,31)(15,35)(16,23)(17,76)(18,33)(19,52)(20,72)(21,66)(22,50)(24,69)(25,48)
(26,59)(27,45)(28,58)(29,51)(30,47)(34,43)(36,44)(37,65)(38,64)(39,49)(40,68)
(46,53)(56,78)(57,80)(60,77)(62,74)(63,79)(67,73)(71,75);;
s2 := ( 2,21)( 3,22)( 4,80)( 5,37)( 6,11)( 7,44)( 8,63)( 9,48)(10,13)(12,70)
(14,61)(16,58)(17,68)(18,69)(19,45)(20,34)(23,52)(24,40)(26,33)(27,32)(28,79)
(29,76)(30,74)(31,42)(35,41)(36,54)(38,55)(39,75)(43,46)(47,66)(49,71)(50,57)
(51,59)(53,73)(56,72)(60,67)(62,65)(77,78);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(82)!( 2,26)( 3,75)( 4,80)( 5,41)( 6,70)( 7,68)( 8,43)( 9,19)(10,13)
(11,12)(15,64)(17,44)(18,47)(21,33)(22,39)(23,42)(24,78)(27,36)(28,79)(29,55)
(30,53)(31,52)(32,54)(35,37)(38,76)(40,77)(45,48)(46,63)(49,62)(50,72)(51,59)
(56,57)(60,67)(65,71)(66,69)(73,74);
s1 := Sym(82)!( 1, 6)( 2,13)( 3,70)( 4,61)( 5,10)( 7,54)( 8,32)( 9,41)(11,55)
(12,42)(14,31)(15,35)(16,23)(17,76)(18,33)(19,52)(20,72)(21,66)(22,50)(24,69)
(25,48)(26,59)(27,45)(28,58)(29,51)(30,47)(34,43)(36,44)(37,65)(38,64)(39,49)
(40,68)(46,53)(56,78)(57,80)(60,77)(62,74)(63,79)(67,73)(71,75);
s2 := Sym(82)!( 2,21)( 3,22)( 4,80)( 5,37)( 6,11)( 7,44)( 8,63)( 9,48)(10,13)
(12,70)(14,61)(16,58)(17,68)(18,69)(19,45)(20,34)(23,52)(24,40)(26,33)(27,32)
(28,79)(29,76)(30,74)(31,42)(35,41)(36,54)(38,55)(39,75)(43,46)(47,66)(49,71)
(50,57)(51,59)(53,73)(56,72)(60,67)(62,65)(77,78);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1 >; 
 

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