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Polytope of Type {2,2,14,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,14,8,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1083341)
Rank : 6
Schlafli Type : {2,2,14,8,2}
Number of vertices, edges, etc : 2, 2, 14, 56, 8, 2
Order of s0s1s2s3s4s5 : 56
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 : {2,2,14,4,2}*896
   4-fold quotients : {2,2,14,2,2}*448
   7-fold quotients : {2,2,2,8,2}*256
   8-fold quotients : {2,2,7,2,2}*224
   14-fold quotients : {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 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)
(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)(50,51)
(55,60)(56,59)(57,58);;
s3 := ( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,27)(20,26)(21,32)(22,31)
(23,30)(24,29)(25,28)(33,48)(34,47)(35,53)(36,52)(37,51)(38,50)(39,49)(40,55)
(41,54)(42,60)(43,59)(44,58)(45,57)(46,56);;
s4 := ( 5,33)( 6,34)( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)
(15,43)(16,44)(17,45)(18,46)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)(25,60)
(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53);;
s5 := (61,62);;
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, 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, 
s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(62)!(1,2);
s1 := Sym(62)!(3,4);
s2 := Sym(62)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)
(27,32)(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)
(50,51)(55,60)(56,59)(57,58);
s3 := Sym(62)!( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,27)(20,26)(21,32)
(22,31)(23,30)(24,29)(25,28)(33,48)(34,47)(35,53)(36,52)(37,51)(38,50)(39,49)
(40,55)(41,54)(42,60)(43,59)(44,58)(45,57)(46,56);
s4 := Sym(62)!( 5,33)( 6,34)( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)
(14,42)(15,43)(16,44)(17,45)(18,46)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)
(25,60)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53);
s5 := Sym(62)!(61,62);
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, 
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, s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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