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Polytope of Type {2,2,2,4,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,4,28}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076200)
Rank : 6
Schlafli Type : {2,2,2,4,28}
Number of vertices, edges, etc : 2, 2, 2, 4, 56, 28
Order of s0s1s2s3s4s5 : 28
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,2,2,2,28}*896, {2,2,2,4,14}*896
   4-fold quotients : {2,2,2,2,14}*448
   7-fold quotients : {2,2,2,4,4}*256
   8-fold quotients : {2,2,2,2,7}*224
   14-fold quotients : {2,2,2,2,4}*128, {2,2,2,4,2}*128
   28-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(41,48)(49,56)(50,57)(51,58)
(52,59)(53,60)(54,61)(55,62);;
s4 := ( 7,35)( 8,41)( 9,40)(10,39)(11,38)(12,37)(13,36)(14,42)(15,48)(16,47)
(17,46)(18,45)(19,44)(20,43)(21,49)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)
(28,56)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57);;
s5 := ( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,22)(23,27)(24,26)(28,29)
(30,34)(31,33)(35,50)(36,49)(37,55)(38,54)(39,53)(40,52)(41,51)(42,57)(43,56)
(44,62)(45,61)(46,60)(47,59)(48,58);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(62)!(1,2);
s1 := Sym(62)!(3,4);
s2 := Sym(62)!(5,6);
s3 := Sym(62)!(35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(41,48)(49,56)(50,57)
(51,58)(52,59)(53,60)(54,61)(55,62);
s4 := Sym(62)!( 7,35)( 8,41)( 9,40)(10,39)(11,38)(12,37)(13,36)(14,42)(15,48)
(16,47)(17,46)(18,45)(19,44)(20,43)(21,49)(22,55)(23,54)(24,53)(25,52)(26,51)
(27,50)(28,56)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57);
s5 := Sym(62)!( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,22)(23,27)(24,26)
(28,29)(30,34)(31,33)(35,50)(36,49)(37,55)(38,54)(39,53)(40,52)(41,51)(42,57)
(43,56)(44,62)(45,61)(46,60)(47,59)(48,58);
poly := sub<Sym(62)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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