Polytope of Type {4,2,7,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,7,2}*224
if this polytope has a name.
Group : SmallGroup(224,178)
Rank : 5
Schlafli Type : {4,2,7,2}
Number of vertices, edges, etc : 4, 4, 7, 7, 2
Order of s₀s₁s₂s₃s₄ : 28
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,7,2,2} of size 448
   {4,2,7,2,3} of size 672
   {4,2,7,2,4} of size 896
   {4,2,7,2,5} of size 1120
   {4,2,7,2,6} of size 1344
   {4,2,7,2,7} of size 1568
   {4,2,7,2,8} of size 1792
Vertex Figure Of :
   {2,4,2,7,2} of size 448
   {3,4,2,7,2} of size 672
   {4,4,2,7,2} of size 896
   {6,4,2,7,2} of size 1344
   {3,4,2,7,2} of size 1344
   {6,4,2,7,2} of size 1344
   {6,4,2,7,2} of size 1344
   {8,4,2,7,2} of size 1792
   {8,4,2,7,2} of size 1792
   {4,4,2,7,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,7,2}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,7,2}*448, {4,2,14,2}*448
   3-fold covers : {12,2,7,2}*672, {4,2,21,2}*672
   4-fold covers : {16,2,7,2}*896, {4,2,28,2}*896, {4,4,14,2}*896, {4,2,14,4}*896, {8,2,14,2}*896
   5-fold covers : {20,2,7,2}*1120, {4,2,35,2}*1120
   6-fold covers : {24,2,7,2}*1344, {8,2,21,2}*1344, {12,2,14,2}*1344, {4,2,14,6}*1344, {4,6,14,2}*1344a, {4,2,42,2}*1344
   7-fold covers : {4,2,49,2}*1568, {28,2,7,2}*1568, {4,2,7,14}*1568, {4,14,7,2}*1568
   8-fold covers : {32,2,7,2}*1792, {4,4,28,2}*1792, {4,4,14,4}*1792, {4,2,28,4}*1792, {4,8,14,2}*1792a, {8,4,14,2}*1792a, {4,8,14,2}*1792b, {8,4,14,2}*1792b, {4,4,14,2}*1792, {4,2,14,8}*1792, {8,2,14,4}*1792, {8,2,28,2}*1792, {4,2,56,2}*1792, {16,2,14,2}*1792
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,11);;
s3 := ( 5, 6)( 7, 8)( 9,10);;
s4 := (12,13);;
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, 
s1*s2*s1*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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!(2,3);
s1 := Sym(13)!(1,2)(3,4);
s2 := Sym(13)!( 6, 7)( 8, 9)(10,11);
s3 := Sym(13)!( 5, 6)( 7, 8)( 9,10);
s4 := Sym(13)!(12,13);
poly := sub<Sym(13)|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, s1*s2*s1*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, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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