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Polytope of Type {4,28,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,28,2}*448
if this polytope has a name.
Group : SmallGroup(448,940)
Rank : 4
Schlafli Type : {4,28,2}
Number of vertices, edges, etc : 4, 56, 28, 2
Order of s0s1s2s3 : 28
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,28,2,2} of size 896
   {4,28,2,3} of size 1344
   {4,28,2,4} of size 1792
Vertex Figure Of :
   {2,4,28,2} of size 896
   {4,4,28,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,28,2}*224, {4,14,2}*224
   4-fold quotients : {2,14,2}*112
   7-fold quotients : {4,4,2}*64
   8-fold quotients : {2,7,2}*56
   14-fold quotients : {2,4,2}*32, {4,2,2}*32
   28-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,28,4}*896, {4,56,2}*896a, {4,28,2}*896, {4,56,2}*896b, {8,28,2}*896a, {8,28,2}*896b
   3-fold covers : {4,28,6}*1344, {12,28,2}*1344, {4,84,2}*1344a
   4-fold covers : {8,28,2}*1792a, {4,56,2}*1792a, {8,56,2}*1792a, {8,56,2}*1792b, {8,56,2}*1792c, {8,56,2}*1792d, {4,28,8}*1792a, {8,28,4}*1792a, {4,28,8}*1792b, {8,28,4}*1792b, {4,56,4}*1792a, {4,28,4}*1792a, {4,28,4}*1792b, {4,56,4}*1792b, {4,56,4}*1792c, {4,56,4}*1792d, {16,28,2}*1792a, {4,112,2}*1792a, {16,28,2}*1792b, {4,112,2}*1792b, {4,28,2}*1792, {4,56,2}*1792b, {8,28,2}*1792b
Permutation Representation (GAP) :
s0 := (29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)
(46,53)(47,54)(48,55)(49,56);;
s1 := ( 1,29)( 2,35)( 3,34)( 4,33)( 5,32)( 6,31)( 7,30)( 8,36)( 9,42)(10,41)
(11,40)(12,39)(13,38)(14,37)(15,43)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)
(22,50)(23,56)(24,55)(25,54)(26,53)(27,52)(28,51);;
s2 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)(10,14)(11,13)(15,16)(17,21)(18,20)(22,23)
(24,28)(25,27)(29,44)(30,43)(31,49)(32,48)(33,47)(34,46)(35,45)(36,51)(37,50)
(38,56)(39,55)(40,54)(41,53)(42,52);;
s3 := (57,58);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
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(58)!(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)
(45,52)(46,53)(47,54)(48,55)(49,56);
s1 := Sym(58)!( 1,29)( 2,35)( 3,34)( 4,33)( 5,32)( 6,31)( 7,30)( 8,36)( 9,42)
(10,41)(11,40)(12,39)(13,38)(14,37)(15,43)(16,49)(17,48)(18,47)(19,46)(20,45)
(21,44)(22,50)(23,56)(24,55)(25,54)(26,53)(27,52)(28,51);
s2 := Sym(58)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)(10,14)(11,13)(15,16)(17,21)(18,20)
(22,23)(24,28)(25,27)(29,44)(30,43)(31,49)(32,48)(33,47)(34,46)(35,45)(36,51)
(37,50)(38,56)(39,55)(40,54)(41,53)(42,52);
s3 := Sym(58)!(57,58);
poly := sub<Sym(58)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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 >; 
 

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