Polytope of Type {7,2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,4,12}*1344c
if this polytope has a name.
Group : SmallGroup(1344,11327)
Rank : 5
Schlafli Type : {7,2,4,12}
Number of vertices, edges, etc : 7, 7, 4, 24, 12
Order of s₀s₁s₂s₃s₄ : 84
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {7,2,4,6}*672c
   4-fold quotients : {7,2,4,3}*336
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 := ( 8,28)( 9,20)(10,17)(11,42)(12,43)(13,14)(15,34)(16,35)(18,29)(19,30)
(21,26)(22,27)(23,54)(24,55)(25,53)(31,49)(32,51)(33,47)(36,52)(37,50)(38,48)
(39,46)(40,44)(41,45);;
s3 := ( 9,10)(11,12)(13,23)(15,19)(16,18)(17,31)(20,36)(21,39)(22,24)(25,41)
(26,27)(28,44)(29,47)(30,37)(32,35)(33,51)(34,48)(38,50)(42,53)(43,45)(46,55)
(49,52);;
s4 := ( 8,16)( 9,12)(10,27)(11,15)(13,30)(14,19)(17,22)(18,26)(20,43)(21,29)
(23,33)(24,50)(25,36)(28,35)(31,46)(32,41)(34,42)(37,55)(38,44)(39,49)(40,48)
(45,51)(47,54)(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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*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)!( 8,28)( 9,20)(10,17)(11,42)(12,43)(13,14)(15,34)(16,35)(18,29)
(19,30)(21,26)(22,27)(23,54)(24,55)(25,53)(31,49)(32,51)(33,47)(36,52)(37,50)
(38,48)(39,46)(40,44)(41,45);
s3 := Sym(55)!( 9,10)(11,12)(13,23)(15,19)(16,18)(17,31)(20,36)(21,39)(22,24)
(25,41)(26,27)(28,44)(29,47)(30,37)(32,35)(33,51)(34,48)(38,50)(42,53)(43,45)
(46,55)(49,52);
s4 := Sym(55)!( 8,16)( 9,12)(10,27)(11,15)(13,30)(14,19)(17,22)(18,26)(20,43)
(21,29)(23,33)(24,50)(25,36)(28,35)(31,46)(32,41)(34,42)(37,55)(38,44)(39,49)
(40,48)(45,51)(47,54)(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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s3 >;

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