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

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

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