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Polytope of Type {2,2,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,56}*448
if this polytope has a name.
Group : SmallGroup(448,1193)
Rank : 4
Schlafli Type : {2,2,56}
Number of vertices, edges, etc : 2, 2, 56, 56
Order of s0s1s2s3 : 56
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,56,2} of size 896
   {2,2,56,4} of size 1792
   {2,2,56,4} of size 1792
Vertex Figure Of :
   {2,2,2,56} of size 896
   {3,2,2,56} of size 1344
   {4,2,2,56} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,28}*224
   4-fold quotients : {2,2,14}*112
   7-fold quotients : {2,2,8}*64
   8-fold quotients : {2,2,7}*56
   14-fold quotients : {2,2,4}*32
   28-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,56}*896a, {4,2,56}*896, {2,2,112}*896
   3-fold covers : {2,6,56}*1344, {6,2,56}*1344, {2,2,168}*1344
   4-fold covers : {2,4,56}*1792a, {2,8,56}*1792b, {2,8,56}*1792c, {8,2,56}*1792, {4,4,56}*1792a, {2,4,112}*1792a, {2,4,112}*1792b, {4,2,112}*1792, {2,2,224}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,25)(20,24)(21,27)
(22,26)(28,29)(31,38)(32,37)(33,40)(34,39)(35,42)(36,41)(43,44)(45,50)(46,49)
(47,52)(48,51)(53,54)(55,58)(56,57)(59,60);;
s3 := ( 5,11)( 6, 8)( 7,19)( 9,21)(10,14)(12,16)(13,31)(15,33)(17,35)(18,24)
(20,26)(22,28)(23,43)(25,45)(27,47)(29,36)(30,37)(32,39)(34,41)(38,53)(40,55)
(42,48)(44,49)(46,51)(50,59)(52,56)(54,57)(58,60);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(60)!(1,2);
s1 := Sym(60)!(3,4);
s2 := Sym(60)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,25)(20,24)
(21,27)(22,26)(28,29)(31,38)(32,37)(33,40)(34,39)(35,42)(36,41)(43,44)(45,50)
(46,49)(47,52)(48,51)(53,54)(55,58)(56,57)(59,60);
s3 := Sym(60)!( 5,11)( 6, 8)( 7,19)( 9,21)(10,14)(12,16)(13,31)(15,33)(17,35)
(18,24)(20,26)(22,28)(23,43)(25,45)(27,47)(29,36)(30,37)(32,39)(34,41)(38,53)
(40,55)(42,48)(44,49)(46,51)(50,59)(52,56)(54,57)(58,60);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*s2*s3 >; 
 

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