Polytope of Type {7,2,8,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,8,3}*1344
if this polytope has a name.
Group : SmallGroup(1344,11355)
Rank : 5
Schlafli Type : {7,2,8,3}
Number of vertices, edges, etc : 7, 7, 16, 24, 6
Order of s₀s₁s₂s₃s₄ : 84
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {7,2,4,3}*672
   4-fold quotients : {7,2,4,3}*336
   8-fold quotients : {7,2,2,3}*168
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 8,18)( 9,14)(10,13)(11,34)(12,36)(15,19)(16,23)(17,25)(20,22)(21,24)
(26,51)(27,55)(28,50)(29,53)(30,54)(31,52)(32,35)(33,37)(38,46)(39,48)(40,44)
(41,47)(42,49)(43,45);;
s3 := ( 9,10)(11,12)(13,26)(14,29)(16,21)(17,20)(18,38)(19,41)(22,44)(23,45)
(24,30)(25,27)(28,49)(31,48)(32,33)(34,50)(35,52)(36,39)(37,42)(40,54)(43,55)
(46,47);;
s4 := ( 8,12)( 9,21)(10,17)(13,25)(14,24)(15,33)(16,20)(18,36)(19,37)(22,23)
(26,28)(27,49)(29,31)(30,48)(38,40)(39,54)(41,43)(42,55)(44,46)(45,47)(50,51)
(52,53);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*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(55)!(2,3)(4,5)(6,7);
s1 := Sym(55)!(1,2)(3,4)(5,6);
s2 := Sym(55)!( 8,18)( 9,14)(10,13)(11,34)(12,36)(15,19)(16,23)(17,25)(20,22)
(21,24)(26,51)(27,55)(28,50)(29,53)(30,54)(31,52)(32,35)(33,37)(38,46)(39,48)
(40,44)(41,47)(42,49)(43,45);
s3 := Sym(55)!( 9,10)(11,12)(13,26)(14,29)(16,21)(17,20)(18,38)(19,41)(22,44)
(23,45)(24,30)(25,27)(28,49)(31,48)(32,33)(34,50)(35,52)(36,39)(37,42)(40,54)
(43,55)(46,47);
s4 := Sym(55)!( 8,12)( 9,21)(10,17)(13,25)(14,24)(15,33)(16,20)(18,36)(19,37)
(22,23)(26,28)(27,49)(29,31)(30,48)(38,40)(39,54)(41,43)(42,55)(44,46)(45,47)
(50,51)(52,53);
poly := sub<Sym(55)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, 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, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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