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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,7,2}*224
if this polytope has a name.
Group : SmallGroup(224,196)
Rank : 6
Schlafli Type : {2,2,2,7,2}
Number of vertices, edges, etc : 2, 2, 2, 7, 7, 2
Order of s0s1s2s3s4s5 : 14
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,7,2,2} of size 448
   {2,2,2,7,2,3} of size 672
   {2,2,2,7,2,4} of size 896
   {2,2,2,7,2,5} of size 1120
   {2,2,2,7,2,6} of size 1344
   {2,2,2,7,2,7} of size 1568
   {2,2,2,7,2,8} of size 1792
Vertex Figure Of :
   {2,2,2,2,7,2} of size 448
   {3,2,2,2,7,2} of size 672
   {4,2,2,2,7,2} of size 896
   {5,2,2,2,7,2} of size 1120
   {6,2,2,2,7,2} of size 1344
   {7,2,2,2,7,2} of size 1568
   {8,2,2,2,7,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,2,7,2}*448, {4,2,2,7,2}*448, {2,2,2,14,2}*448
   3-fold covers : {2,6,2,7,2}*672, {6,2,2,7,2}*672, {2,2,2,21,2}*672
   4-fold covers : {4,4,2,7,2}*896, {2,8,2,7,2}*896, {8,2,2,7,2}*896, {2,2,2,28,2}*896, {2,2,2,14,4}*896, {2,2,4,14,2}*896, {2,4,2,14,2}*896, {4,2,2,14,2}*896
   5-fold covers : {2,10,2,7,2}*1120, {10,2,2,7,2}*1120, {2,2,2,35,2}*1120
   6-fold covers : {2,12,2,7,2}*1344, {12,2,2,7,2}*1344, {4,6,2,7,2}*1344a, {6,4,2,7,2}*1344a, {2,4,2,21,2}*1344, {4,2,2,21,2}*1344, {2,2,2,14,6}*1344, {2,2,6,14,2}*1344, {2,6,2,14,2}*1344, {6,2,2,14,2}*1344, {2,2,2,42,2}*1344
   7-fold covers : {2,2,2,49,2}*1568, {2,2,2,7,14}*1568, {2,2,14,7,2}*1568, {2,14,2,7,2}*1568, {14,2,2,7,2}*1568
   8-fold covers : {4,8,2,7,2}*1792a, {8,4,2,7,2}*1792a, {4,8,2,7,2}*1792b, {8,4,2,7,2}*1792b, {4,4,2,7,2}*1792, {2,16,2,7,2}*1792, {16,2,2,7,2}*1792, {2,4,4,14,2}*1792, {4,4,2,14,2}*1792, {2,2,2,28,4}*1792, {2,2,4,28,2}*1792, {2,4,2,14,4}*1792, {4,2,2,14,4}*1792, {4,2,4,14,2}*1792, {2,2,4,14,4}*1792, {2,4,2,28,2}*1792, {4,2,2,28,2}*1792, {2,2,2,14,8}*1792, {2,2,8,14,2}*1792, {2,8,2,14,2}*1792, {8,2,2,14,2}*1792, {2,2,2,56,2}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(12,13);;
s4 := ( 7, 8)( 9,10)(11,12);;
s5 := (14,15);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(15)!(1,2);
s1 := Sym(15)!(3,4);
s2 := Sym(15)!(5,6);
s3 := Sym(15)!( 8, 9)(10,11)(12,13);
s4 := Sym(15)!( 7, 8)( 9,10)(11,12);
s5 := Sym(15)!(14,15);
poly := sub<Sym(15)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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