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Polytope of Type {2,2,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,28}*224
if this polytope has a name.
Group : SmallGroup(224,176)
Rank : 4
Schlafli Type : {2,2,28}
Number of vertices, edges, etc : 2, 2, 28, 28
Order of s0s1s2s3 : 28
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,28,2} of size 448
   {2,2,28,4} of size 896
   {2,2,28,6} of size 1344
   {2,2,28,6} of size 1344
   {2,2,28,8} of size 1792
   {2,2,28,8} of size 1792
   {2,2,28,4} of size 1792
Vertex Figure Of :
   {2,2,2,28} of size 448
   {3,2,2,28} of size 672
   {4,2,2,28} of size 896
   {5,2,2,28} of size 1120
   {6,2,2,28} of size 1344
   {7,2,2,28} of size 1568
   {8,2,2,28} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,14}*112
   4-fold quotients : {2,2,7}*56
   7-fold quotients : {2,2,4}*32
   14-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,28}*448, {4,2,28}*448, {2,2,56}*448
   3-fold covers : {2,6,28}*672a, {6,2,28}*672, {2,2,84}*672
   4-fold covers : {4,4,28}*896, {2,4,56}*896a, {2,4,28}*896, {2,4,56}*896b, {2,8,28}*896a, {2,8,28}*896b, {4,2,56}*896, {8,2,28}*896, {2,2,112}*896
   5-fold covers : {2,10,28}*1120, {10,2,28}*1120, {2,2,140}*1120
   6-fold covers : {12,2,28}*1344, {4,6,28}*1344a, {6,4,28}*1344, {2,6,56}*1344, {6,2,56}*1344, {2,12,28}*1344, {2,4,84}*1344a, {4,2,84}*1344, {2,2,168}*1344
   7-fold covers : {2,2,196}*1568, {2,14,28}*1568a, {2,14,28}*1568b, {14,2,28}*1568
   8-fold covers : {2,8,28}*1792a, {2,4,56}*1792a, {2,8,56}*1792a, {2,8,56}*1792b, {2,8,56}*1792c, {2,8,56}*1792d, {8,2,56}*1792, {8,4,28}*1792a, {4,4,56}*1792a, {8,4,28}*1792b, {4,4,56}*1792b, {4,8,28}*1792a, {4,4,28}*1792a, {4,4,28}*1792b, {4,8,28}*1792b, {4,8,28}*1792c, {4,8,28}*1792d, {2,16,28}*1792a, {2,4,112}*1792a, {2,16,28}*1792b, {2,4,112}*1792b, {2,4,28}*1792, {2,4,56}*1792b, {2,8,28}*1792b, {16,2,28}*1792, {4,2,112}*1792, {2,2,224}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)(25,26)
(27,30)(28,29)(31,32);;
s3 := ( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)(20,23)
(22,31)(24,28)(26,29)(30,32);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(32)!(1,2);
s1 := Sym(32)!(3,4);
s2 := Sym(32)!( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)
(25,26)(27,30)(28,29)(31,32);
s3 := Sym(32)!( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)
(20,23)(22,31)(24,28)(26,29)(30,32);
poly := sub<Sym(32)|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 >; 
 

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