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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,4,2}*448
if this polytope has a name.
Group : SmallGroup(448,1369)
Rank : 5
Schlafli Type : {2,14,4,2}
Number of vertices, edges, etc : 2, 14, 28, 4, 2
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,4,2,2} of size 896
   {2,14,4,2,3} of size 1344
   {2,14,4,2,4} of size 1792
Vertex Figure Of :
   {2,2,14,4,2} of size 896
   {3,2,14,4,2} of size 1344
   {4,2,14,4,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,2,2}*224
   4-fold quotients : {2,7,2,2}*112
   7-fold quotients : {2,2,4,2}*64
   14-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,28,4,2}*896, {2,14,4,4}*896, {4,14,4,2}*896, {2,14,8,2}*896
   3-fold covers : {2,14,12,2}*1344, {2,14,4,6}*1344, {6,14,4,2}*1344, {2,42,4,2}*1344a
   4-fold covers : {2,28,4,4}*1792, {4,28,4,2}*1792, {4,14,4,4}*1792, {2,14,4,8}*1792a, {2,14,8,4}*1792a, {2,28,8,2}*1792a, {2,56,4,2}*1792a, {2,14,4,8}*1792b, {2,14,8,4}*1792b, {2,28,8,2}*1792b, {2,56,4,2}*1792b, {2,14,4,4}*1792, {2,28,4,2}*1792, {4,14,8,2}*1792, {8,14,4,2}*1792, {2,14,16,2}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 8, 9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)
(27,28)(29,30);;
s2 := ( 3, 5)( 4,13)( 6,10)( 7, 8)( 9,21)(11,17)(12,19)(14,15)(16,27)(20,25)
(22,23)(24,28)(26,29);;
s3 := ( 3, 4)( 5, 8)( 6, 9)( 7,12)(10,15)(11,16)(13,19)(14,20)(17,23)(18,24)
(21,25)(22,26)(27,29)(28,30);;
s4 := (31,32);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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(32)!(1,2);
s1 := Sym(32)!( 5, 6)( 8, 9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28)(29,30);
s2 := Sym(32)!( 3, 5)( 4,13)( 6,10)( 7, 8)( 9,21)(11,17)(12,19)(14,15)(16,27)
(20,25)(22,23)(24,28)(26,29);
s3 := Sym(32)!( 3, 4)( 5, 8)( 6, 9)( 7,12)(10,15)(11,16)(13,19)(14,20)(17,23)
(18,24)(21,25)(22,26)(27,29)(28,30);
s4 := Sym(32)!(31,32);
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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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