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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,7,2}*112
if this polytope has a name.
Group : SmallGroup(112,42)
Rank : 5
Schlafli Type : {2,2,7,2}
Number of vertices, edges, etc : 2, 2, 7, 7, 2
Order of s₀s₁s₂s₃s₄ : 14
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,7,2,2} of size 224
   {2,2,7,2,3} of size 336
   {2,2,7,2,4} of size 448
   {2,2,7,2,5} of size 560
   {2,2,7,2,6} of size 672
   {2,2,7,2,7} of size 784
   {2,2,7,2,8} of size 896
   {2,2,7,2,9} of size 1008
   {2,2,7,2,10} of size 1120
   {2,2,7,2,11} of size 1232
   {2,2,7,2,12} of size 1344
   {2,2,7,2,13} of size 1456
   {2,2,7,2,14} of size 1568
   {2,2,7,2,15} of size 1680
   {2,2,7,2,16} of size 1792
   {2,2,7,2,17} of size 1904
Vertex Figure Of :
   {2,2,2,7,2} of size 224
   {3,2,2,7,2} of size 336
   {4,2,2,7,2} of size 448
   {5,2,2,7,2} of size 560
   {6,2,2,7,2} of size 672
   {7,2,2,7,2} of size 784
   {8,2,2,7,2} of size 896
   {9,2,2,7,2} of size 1008
   {10,2,2,7,2} of size 1120
   {11,2,2,7,2} of size 1232
   {12,2,2,7,2} of size 1344
   {13,2,2,7,2} of size 1456
   {14,2,2,7,2} of size 1568
   {15,2,2,7,2} of size 1680
   {16,2,2,7,2} of size 1792
   {17,2,2,7,2} of size 1904
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,7,2}*224, {2,2,14,2}*224
   3-fold covers : {6,2,7,2}*336, {2,2,21,2}*336
   4-fold covers : {8,2,7,2}*448, {2,2,28,2}*448, {2,2,14,4}*448, {2,4,14,2}*448, {4,2,14,2}*448
   5-fold covers : {10,2,7,2}*560, {2,2,35,2}*560
   6-fold covers : {12,2,7,2}*672, {4,2,21,2}*672, {2,2,14,6}*672, {2,6,14,2}*672, {6,2,14,2}*672, {2,2,42,2}*672
   7-fold covers : {2,2,49,2}*784, {2,2,7,14}*784, {2,14,7,2}*784, {14,2,7,2}*784
   8-fold covers : {16,2,7,2}*896, {2,2,28,4}*896, {2,4,28,2}*896, {4,2,28,2}*896, {4,4,14,2}*896, {2,4,14,4}*896, {4,2,14,4}*896, {2,2,56,2}*896, {2,2,14,8}*896, {2,8,14,2}*896, {8,2,14,2}*896
   9-fold covers : {18,2,7,2}*1008, {2,2,63,2}*1008, {2,2,21,6}*1008, {2,6,21,2}*1008, {6,2,21,2}*1008
   10-fold covers : {20,2,7,2}*1120, {4,2,35,2}*1120, {2,2,14,10}*1120, {2,10,14,2}*1120, {10,2,14,2}*1120, {2,2,70,2}*1120
   11-fold covers : {22,2,7,2}*1232, {2,2,77,2}*1232
   12-fold covers : {24,2,7,2}*1344, {8,2,21,2}*1344, {2,2,14,12}*1344, {2,12,14,2}*1344, {12,2,14,2}*1344, {2,2,28,6}*1344a, {2,6,28,2}*1344a, {6,2,28,2}*1344, {2,4,14,6}*1344, {2,6,14,4}*1344, {4,2,14,6}*1344, {4,6,14,2}*1344a, {6,2,14,4}*1344, {6,4,14,2}*1344, {2,2,84,2}*1344, {2,2,42,4}*1344a, {2,4,42,2}*1344a, {4,2,42,2}*1344, {2,2,21,6}*1344, {2,6,21,2}*1344, {2,2,21,4}*1344, {2,4,21,2}*1344
   13-fold covers : {26,2,7,2}*1456, {2,2,91,2}*1456
   14-fold covers : {4,2,49,2}*1568, {2,2,98,2}*1568, {28,2,7,2}*1568, {4,2,7,14}*1568, {4,14,7,2}*1568, {2,2,14,14}*1568a, {2,2,14,14}*1568c, {2,14,14,2}*1568a, {2,14,14,2}*1568b, {14,2,14,2}*1568
   15-fold covers : {30,2,7,2}*1680, {10,2,21,2}*1680, {6,2,35,2}*1680, {2,2,105,2}*1680
   16-fold covers : {32,2,7,2}*1792, {4,4,28,2}*1792, {2,4,28,4}*1792, {4,4,14,4}*1792, {4,2,28,4}*1792, {4,8,14,2}*1792a, {8,4,14,2}*1792a, {2,2,28,8}*1792a, {2,8,28,2}*1792a, {2,2,56,4}*1792a, {2,4,56,2}*1792a, {4,8,14,2}*1792b, {8,4,14,2}*1792b, {2,2,28,8}*1792b, {2,8,28,2}*1792b, {2,2,56,4}*1792b, {2,4,56,2}*1792b, {4,4,14,2}*1792, {2,2,28,4}*1792, {2,4,28,2}*1792, {4,2,14,8}*1792, {8,2,14,4}*1792, {2,4,14,8}*1792, {2,8,14,4}*1792, {8,2,28,2}*1792, {4,2,56,2}*1792, {2,2,14,16}*1792, {2,16,14,2}*1792, {16,2,14,2}*1792, {2,2,112,2}*1792
   17-fold covers : {34,2,7,2}*1904, {2,2,119,2}*1904
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (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*s1*s0*s1, 
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!(1,2);
s1 := Sym(13)!(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*s1*s0*s1, 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope