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Polytope of Type {2,2,28,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,28,4}*896
if this polytope has a name.
Group : SmallGroup(896,17525)
Rank : 5
Schlafli Type : {2,2,28,4}
Number of vertices, edges, etc : 2, 2, 28, 56, 4
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,28,4,2} of size 1792
Vertex Figure Of :
   {2,2,2,28,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,28,2}*448, {2,2,14,4}*448
   4-fold quotients : {2,2,14,2}*224
   7-fold quotients : {2,2,4,4}*128
   8-fold quotients : {2,2,7,2}*112
   14-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   28-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,28,4}*1792, {4,2,28,4}*1792, {2,2,28,8}*1792a, {2,2,56,4}*1792a, {2,2,28,8}*1792b, {2,2,56,4}*1792b, {2,2,28,4}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)
(28,31)(29,30)(33,47)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,54)(41,60)
(42,59)(43,58)(44,57)(45,56)(46,55);;
s3 := ( 5,34)( 6,33)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,41)(13,40)(14,46)
(15,45)(16,44)(17,43)(18,42)(19,48)(20,47)(21,53)(22,52)(23,51)(24,50)(25,49)
(26,55)(27,54)(28,60)(29,59)(30,58)(31,57)(32,56);;
s4 := (33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(47,54)(48,55)(49,56)
(50,57)(51,58)(52,59)(53,60);;
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, 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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(60)!(1,2);
s1 := Sym(60)!(3,4);
s2 := Sym(60)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)
(27,32)(28,31)(29,30)(33,47)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,54)
(41,60)(42,59)(43,58)(44,57)(45,56)(46,55);
s3 := Sym(60)!( 5,34)( 6,33)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,41)(13,40)
(14,46)(15,45)(16,44)(17,43)(18,42)(19,48)(20,47)(21,53)(22,52)(23,51)(24,50)
(25,49)(26,55)(27,54)(28,60)(29,59)(30,58)(31,57)(32,56);
s4 := Sym(60)!(33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(47,54)(48,55)
(49,56)(50,57)(51,58)(52,59)(53,60);
poly := sub<Sym(60)|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, 
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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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