Polytope of Type {7,14,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,14,7}*1372
if this polytope has a name.
Group : SmallGroup(1372,16)
Rank : 4
Schlafli Type : {7,14,7}
Number of vertices, edges, etc : 7, 49, 49, 7
Order of s₀s₁s₂s₃ : 7
Order of s₀s₁s₂s₃s₂s₁ : 14
Special Properties :
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {7,2,7}*196
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)(14,44)
(15,36)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,29)(23,35)(24,34)(25,33)
(26,32)(27,31)(28,30);;
s1 := ( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(15,43)(16,49)(17,48)
(18,47)(19,46)(20,45)(21,44)(22,36)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)
(30,35)(31,34)(32,33);;
s2 := ( 2, 7)( 3, 6)( 4, 5)( 8, 9)(10,14)(11,13)(15,17)(18,21)(19,20)(22,25)
(23,24)(26,28)(29,33)(30,32)(34,35)(36,41)(37,40)(38,39)(43,49)(44,48)
(45,47);;
s3 := ( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)
(24,27)(25,26)(30,35)(31,34)(32,33)(37,42)(38,41)(39,40)(44,49)(45,48)
(46,47);;
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*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(49)!( 2, 7)( 3, 6)( 4, 5)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)
(14,44)(15,36)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,29)(23,35)(24,34)
(25,33)(26,32)(27,31)(28,30);
s1 := Sym(49)!( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(15,43)(16,49)
(17,48)(18,47)(19,46)(20,45)(21,44)(22,36)(23,42)(24,41)(25,40)(26,39)(27,38)
(28,37)(30,35)(31,34)(32,33);
s2 := Sym(49)!( 2, 7)( 3, 6)( 4, 5)( 8, 9)(10,14)(11,13)(15,17)(18,21)(19,20)
(22,25)(23,24)(26,28)(29,33)(30,32)(34,35)(36,41)(37,40)(38,39)(43,49)(44,48)
(45,47);
s3 := Sym(49)!( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)
(23,28)(24,27)(25,26)(30,35)(31,34)(32,33)(37,42)(38,41)(39,40)(44,49)(45,48)
(46,47);
poly := sub<Sym(49)|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*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References : None.
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