Polytope of Type {56,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,2,4}*896
if this polytope has a name.
Group : SmallGroup(896,11643)
Rank : 4
Schlafli Type : {56,2,4}
Number of vertices, edges, etc : 56, 56, 4, 4
Order of s₀s₁s₂s₃ : 56
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {56,2,4,2} of size 1792
Vertex Figure Of :
   {2,56,2,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {28,2,4}*448, {56,2,2}*448
   4-fold quotients : {28,2,2}*224, {14,2,4}*224
   7-fold quotients : {8,2,4}*128
   8-fold quotients : {7,2,4}*112, {14,2,2}*112
   14-fold quotients : {4,2,4}*64, {8,2,2}*64
   16-fold quotients : {7,2,2}*56
   28-fold quotients : {2,2,4}*32, {4,2,2}*32
   56-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {56,2,8}*1792, {56,4,4}*1792a, {112,2,4}*1792
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope