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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,2,4}*224
if this polytope has a name.
Group : SmallGroup(224,178)
Rank : 5
Schlafli Type : {7,2,2,4}
Number of vertices, edges, etc : 7, 7, 2, 4, 4
Order of s₀s₁s₂s₃s₄ : 28
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,2,4,2} of size 448
   {7,2,2,4,3} of size 672
   {7,2,2,4,4} of size 896
   {7,2,2,4,6} of size 1344
   {7,2,2,4,3} of size 1344
   {7,2,2,4,6} of size 1344
   {7,2,2,4,6} of size 1344
   {7,2,2,4,8} of size 1792
   {7,2,2,4,8} of size 1792
   {7,2,2,4,4} of size 1792
Vertex Figure Of :
   {2,7,2,2,4} of size 448
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,4,4}*448, {7,2,2,8}*448, {14,2,2,4}*448
   3-fold covers : {7,2,2,12}*672, {7,2,6,4}*672a, {21,2,2,4}*672
   4-fold covers : {7,2,4,8}*896a, {7,2,8,4}*896a, {7,2,4,8}*896b, {7,2,8,4}*896b, {7,2,4,4}*896, {7,2,2,16}*896, {28,2,2,4}*896, {14,2,4,4}*896, {14,4,2,4}*896, {14,2,2,8}*896
   5-fold covers : {7,2,2,20}*1120, {7,2,10,4}*1120, {35,2,2,4}*1120
   6-fold covers : {7,2,4,12}*1344a, {7,2,12,4}*1344a, {7,2,2,24}*1344, {7,2,6,8}*1344, {21,2,4,4}*1344, {21,2,2,8}*1344, {14,2,2,12}*1344, {14,2,6,4}*1344a, {14,6,2,4}*1344, {42,2,2,4}*1344
   7-fold covers : {49,2,2,4}*1568, {7,2,2,28}*1568, {7,2,14,4}*1568, {7,14,2,4}*1568
   8-fold covers : {7,2,4,8}*1792a, {7,2,8,4}*1792a, {7,2,8,8}*1792a, {7,2,8,8}*1792b, {7,2,8,8}*1792c, {7,2,8,8}*1792d, {7,2,4,16}*1792a, {7,2,16,4}*1792a, {7,2,4,16}*1792b, {7,2,16,4}*1792b, {7,2,4,4}*1792, {7,2,4,8}*1792b, {7,2,8,4}*1792b, {7,2,2,32}*1792, {14,4,4,4}*1792, {28,2,4,4}*1792, {28,4,2,4}*1792, {14,2,4,8}*1792a, {14,2,8,4}*1792a, {14,2,4,8}*1792b, {14,2,8,4}*1792b, {14,2,4,4}*1792, {14,4,2,8}*1792, {14,8,2,4}*1792, {28,2,2,8}*1792, {56,2,2,4}*1792, {14,2,2,16}*1792
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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