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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4,2,2}*448
if this polytope has a name.
Group : SmallGroup(448,1369)
Rank : 5
Schlafli Type : {14,4,2,2}
Number of vertices, edges, etc : 14, 28, 4, 2, 2
Order of s₀s₁s₂s₃s₄ : 28
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,4,2,2,2} of size 896
   {14,4,2,2,3} of size 1344
   {14,4,2,2,4} of size 1792
Vertex Figure Of :
   {2,14,4,2,2} of size 896
   {4,14,4,2,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {14,2,2,2}*224
   4-fold quotients : {7,2,2,2}*112
   7-fold quotients : {2,4,2,2}*64
   14-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,4,2,2}*896, {14,4,4,2}*896, {14,4,2,4}*896, {14,8,2,2}*896
   3-fold covers : {14,12,2,2}*1344, {14,4,2,6}*1344, {14,4,6,2}*1344, {42,4,2,2}*1344a
   4-fold covers : {14,4,4,4}*1792, {28,4,4,2}*1792, {28,4,2,4}*1792, {14,4,8,2}*1792a, {14,8,4,2}*1792a, {28,8,2,2}*1792a, {56,4,2,2}*1792a, {14,4,8,2}*1792b, {14,8,4,2}*1792b, {28,8,2,2}*1792b, {56,4,2,2}*1792b, {14,4,4,2}*1792, {28,4,2,2}*1792, {14,4,2,8}*1792, {14,8,2,4}*1792, {14,16,2,2}*1792
Permutation Representation (GAP) :

s0 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)(18,23)
(20,21)(22,26)(24,27);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)(16,22)
(19,23)(20,24)(25,27)(26,28);;
s3 := (29,30);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28);
s1 := Sym(32)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)
(18,23)(20,21)(22,26)(24,27);
s2 := Sym(32)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)
(16,22)(19,23)(20,24)(25,27)(26,28);
s3 := Sym(32)!(29,30);
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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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