Polytope of Type {7,2,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,56}*1568
if this polytope has a name.
Group : SmallGroup(1568,397)
Rank : 4
Schlafli Type : {7,2,56}
Number of vertices, edges, etc : 7, 7, 56, 56
Order of s₀s₁s₂s₃ : 56
Order of s₀s₁s₂s₃s₂s₁ : 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 : {7,2,28}*784
   4-fold quotients : {7,2,14}*392
   7-fold quotients : {7,2,8}*224
   8-fold quotients : {7,2,7}*196
   14-fold quotients : {7,2,4}*112
   28-fold quotients : {7,2,2}*56
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)(13,16)(14,18)(15,17)(19,20)(21,26)(22,28)(23,27)(24,30)
(25,29)(31,32)(34,41)(35,40)(36,43)(37,42)(38,45)(39,44)(46,47)(48,53)(49,52)
(50,55)(51,54)(56,57)(58,61)(59,60)(62,63);;
s3 := ( 8,14)( 9,11)(10,22)(12,24)(13,17)(15,19)(16,34)(18,36)(20,38)(21,27)
(23,29)(25,31)(26,46)(28,48)(30,50)(32,39)(33,40)(35,42)(37,44)(41,56)(43,58)
(45,51)(47,52)(49,54)(53,62)(55,59)(57,60)(61,63);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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(63)!(2,3)(4,5)(6,7);
s1 := Sym(63)!(1,2)(3,4)(5,6);
s2 := Sym(63)!( 9,10)(11,12)(13,16)(14,18)(15,17)(19,20)(21,26)(22,28)(23,27)
(24,30)(25,29)(31,32)(34,41)(35,40)(36,43)(37,42)(38,45)(39,44)(46,47)(48,53)
(49,52)(50,55)(51,54)(56,57)(58,61)(59,60)(62,63);
s3 := Sym(63)!( 8,14)( 9,11)(10,22)(12,24)(13,17)(15,19)(16,34)(18,36)(20,38)
(21,27)(23,29)(25,31)(26,46)(28,48)(30,50)(32,39)(33,40)(35,42)(37,44)(41,56)
(43,58)(45,51)(47,52)(49,54)(53,62)(55,59)(57,60)(61,63);
poly := sub<Sym(63)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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