Polytope of Type {2,56,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,56,2,3}*1344
if this polytope has a name.
Group : SmallGroup(1344,8483)
Rank : 5
Schlafli Type : {2,56,2,3}
Number of vertices, edges, etc : 2, 56, 56, 3, 3
Order of s₀s₁s₂s₃s₄ : 168
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 : {2,28,2,3}*672
   4-fold quotients : {2,14,2,3}*336
   7-fold quotients : {2,8,2,3}*192
   8-fold quotients : {2,7,2,3}*168
   14-fold quotients : {2,4,2,3}*96
   28-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)(19,25)
(20,24)(26,27)(29,36)(30,35)(31,38)(32,37)(33,40)(34,39)(41,42)(43,48)(44,47)
(45,50)(46,49)(51,52)(53,56)(54,55)(57,58);;
s2 := ( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,29)(13,31)(15,33)(16,22)
(18,24)(20,26)(21,41)(23,43)(25,45)(27,34)(28,35)(30,37)(32,39)(36,51)(38,53)
(40,46)(42,47)(44,49)(48,57)(50,54)(52,55)(56,58);;
s3 := (60,61);;
s4 := (59,60);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(61)!(1,2);
s1 := Sym(61)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)
(19,25)(20,24)(26,27)(29,36)(30,35)(31,38)(32,37)(33,40)(34,39)(41,42)(43,48)
(44,47)(45,50)(46,49)(51,52)(53,56)(54,55)(57,58);
s2 := Sym(61)!( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,29)(13,31)(15,33)
(16,22)(18,24)(20,26)(21,41)(23,43)(25,45)(27,34)(28,35)(30,37)(32,39)(36,51)
(38,53)(40,46)(42,47)(44,49)(48,57)(50,54)(52,55)(56,58);
s3 := Sym(61)!(60,61);
s4 := Sym(61)!(59,60);
poly := sub<Sym(61)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope