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

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

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