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Polytope of Type {2,2,14,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,14,4}*448
if this polytope has a name.
Group : SmallGroup(448,1369)
Rank : 5
Schlafli Type : {2,2,14,4}
Number of vertices, edges, etc : 2, 2, 14, 28, 4
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,14,4,2} of size 896
   {2,2,14,4,4} of size 1792
Vertex Figure Of :
   {2,2,2,14,4} of size 896
   {3,2,2,14,4} of size 1344
   {4,2,2,14,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,14,2}*224
   4-fold quotients : {2,2,7,2}*112
   7-fold quotients : {2,2,2,4}*64
   14-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,28,4}*896, {2,4,14,4}*896, {4,2,14,4}*896, {2,2,14,8}*896
   3-fold covers : {2,2,14,12}*1344, {2,6,14,4}*1344, {6,2,14,4}*1344, {2,2,42,4}*1344a
   4-fold covers : {2,4,28,4}*1792, {4,4,14,4}*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, {4,2,14,8}*1792, {8,2,14,4}*1792, {2,4,14,8}*1792, {2,8,14,4}*1792, {2,2,14,16}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30)(31,32);;
s3 := ( 5, 7)( 6,15)( 8,12)( 9,10)(11,23)(13,19)(14,21)(16,17)(18,29)(22,27)
(24,25)(26,30)(28,31);;
s4 := ( 5, 6)( 7,10)( 8,11)( 9,14)(12,17)(13,18)(15,21)(16,22)(19,25)(20,26)
(23,27)(24,28)(29,31)(30,32);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(32)!(1,2);
s1 := Sym(32)!(3,4);
s2 := Sym(32)!( 7, 8)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)
(27,28)(29,30)(31,32);
s3 := Sym(32)!( 5, 7)( 6,15)( 8,12)( 9,10)(11,23)(13,19)(14,21)(16,17)(18,29)
(22,27)(24,25)(26,30)(28,31);
s4 := Sym(32)!( 5, 6)( 7,10)( 8,11)( 9,14)(12,17)(13,18)(15,21)(16,22)(19,25)
(20,26)(23,27)(24,28)(29,31)(30,32);
poly := sub<Sym(32)|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 >; 
 

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