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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,3,8}*1344
if this polytope has a name.
Group : SmallGroup(1344,11355)
Rank : 5
Schlafli Type : {7,2,3,8}
Number of vertices, edges, etc : 7, 7, 6, 24, 16
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 : {7,2,3,4}*672
   4-fold quotients : {7,2,3,4}*336
   8-fold quotients : {7,2,3,2}*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 := ( 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);;
s3 := ( 8,11)( 9,20)(10,16)(13,49)(14,48)(15,32)(17,21)(18,54)(19,55)(22,47)
(23,46)(24,31)(25,28)(26,27)(29,30)(34,51)(35,53)(36,40)(37,43)(38,39)(41,42)
(44,45);;
s4 := ( 8,51)( 9,47)(10,46)(11,54)(12,40)(13,41)(14,38)(15,53)(16,49)(17,31)
(18,29)(19,26)(20,48)(21,28)(22,42)(23,39)(24,52)(25,50)(27,34)(30,35)(32,55)
(33,43)(36,45)(37,44);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*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)!( 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);
s3 := Sym(55)!( 8,11)( 9,20)(10,16)(13,49)(14,48)(15,32)(17,21)(18,54)(19,55)
(22,47)(23,46)(24,31)(25,28)(26,27)(29,30)(34,51)(35,53)(36,40)(37,43)(38,39)
(41,42)(44,45);
s4 := Sym(55)!( 8,51)( 9,47)(10,46)(11,54)(12,40)(13,41)(14,38)(15,53)(16,49)
(17,31)(18,29)(19,26)(20,48)(21,28)(22,42)(23,39)(24,52)(25,50)(27,34)(30,35)
(32,55)(33,43)(36,45)(37,44);
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 >;

to this polytope