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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,2,7}*224
if this polytope has a name.
Group : SmallGroup(224,196)
Rank : 6
Schlafli Type : {2,2,2,2,7}
Number of vertices, edges, etc : 2, 2, 2, 2, 7, 7
Order of s₀s₁s₂s₃s₄s₅ : 14
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,2,7,2} of size 448
Vertex Figure Of :
   {2,2,2,2,2,7} of size 448
   {3,2,2,2,2,7} of size 672
   {4,2,2,2,2,7} of size 896
   {5,2,2,2,2,7} of size 1120
   {6,2,2,2,2,7} of size 1344
   {7,2,2,2,2,7} of size 1568
   {8,2,2,2,2,7} of size 1792
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,4,2,7}*448, {2,4,2,2,7}*448, {4,2,2,2,7}*448, {2,2,2,2,14}*448
   3-fold covers : {2,2,6,2,7}*672, {2,6,2,2,7}*672, {6,2,2,2,7}*672, {2,2,2,2,21}*672
   4-fold covers : {2,4,4,2,7}*896, {4,4,2,2,7}*896, {4,2,4,2,7}*896, {2,2,8,2,7}*896, {2,8,2,2,7}*896, {8,2,2,2,7}*896, {2,2,2,2,28}*896, {2,2,2,4,14}*896, {2,2,4,2,14}*896, {2,4,2,2,14}*896, {4,2,2,2,14}*896
   5-fold covers : {2,2,10,2,7}*1120, {2,10,2,2,7}*1120, {10,2,2,2,7}*1120, {2,2,2,2,35}*1120
   6-fold covers : {2,2,12,2,7}*1344, {2,12,2,2,7}*1344, {12,2,2,2,7}*1344, {2,4,6,2,7}*1344a, {2,6,4,2,7}*1344a, {4,2,6,2,7}*1344, {4,6,2,2,7}*1344a, {6,2,4,2,7}*1344, {6,4,2,2,7}*1344a, {2,2,4,2,21}*1344, {2,4,2,2,21}*1344, {4,2,2,2,21}*1344, {2,2,2,6,14}*1344, {2,2,6,2,14}*1344, {2,6,2,2,14}*1344, {6,2,2,2,14}*1344, {2,2,2,2,42}*1344
   7-fold covers : {2,2,2,2,49}*1568, {2,2,2,14,7}*1568, {2,2,14,2,7}*1568, {2,14,2,2,7}*1568, {14,2,2,2,7}*1568
   8-fold covers : {4,4,4,2,7}*1792, {2,4,8,2,7}*1792a, {2,8,4,2,7}*1792a, {4,8,2,2,7}*1792a, {8,4,2,2,7}*1792a, {2,4,8,2,7}*1792b, {2,8,4,2,7}*1792b, {4,8,2,2,7}*1792b, {8,4,2,2,7}*1792b, {2,4,4,2,7}*1792, {4,4,2,2,7}*1792, {4,2,8,2,7}*1792, {8,2,4,2,7}*1792, {2,2,16,2,7}*1792, {2,16,2,2,7}*1792, {16,2,2,2,7}*1792, {2,2,4,4,14}*1792, {2,4,4,2,14}*1792, {4,4,2,2,14}*1792, {2,2,2,4,28}*1792, {2,4,2,4,14}*1792, {4,2,2,4,14}*1792, {4,2,4,2,14}*1792, {2,2,4,2,28}*1792, {2,4,2,2,28}*1792, {4,2,2,2,28}*1792, {2,2,2,8,14}*1792, {2,2,8,2,14}*1792, {2,8,2,2,14}*1792, {8,2,2,2,14}*1792, {2,2,2,2,56}*1792
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (7,8);;
s4 := (10,11)(12,13)(14,15);;
s5 := ( 9,10)(11,12)(13,14);;
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, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!(1,2);
s1 := Sym(15)!(3,4);
s2 := Sym(15)!(5,6);
s3 := Sym(15)!(7,8);
s4 := Sym(15)!(10,11)(12,13)(14,15);
s5 := Sym(15)!( 9,10)(11,12)(13,14);
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, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope