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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,7}*112
if this polytope has a name.
Group : SmallGroup(112,42)
Rank : 5
Schlafli Type : {2,2,2,7}
Number of vertices, edges, etc : 2, 2, 2, 7, 7
Order of s₀s₁s₂s₃s₄ : 14
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,7,2} of size 224
   {2,2,2,7,14} of size 1568
Vertex Figure Of :
   {2,2,2,2,7} of size 224
   {3,2,2,2,7} of size 336
   {4,2,2,2,7} of size 448
   {5,2,2,2,7} of size 560
   {6,2,2,2,7} of size 672
   {7,2,2,2,7} of size 784
   {8,2,2,2,7} of size 896
   {9,2,2,2,7} of size 1008
   {10,2,2,2,7} of size 1120
   {11,2,2,2,7} of size 1232
   {12,2,2,2,7} of size 1344
   {13,2,2,2,7} of size 1456
   {14,2,2,2,7} of size 1568
   {15,2,2,2,7} of size 1680
   {16,2,2,2,7} of size 1792
   {17,2,2,2,7} of size 1904
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,2,7}*224, {4,2,2,7}*224, {2,2,2,14}*224
   3-fold covers : {2,6,2,7}*336, {6,2,2,7}*336, {2,2,2,21}*336
   4-fold covers : {4,4,2,7}*448, {2,8,2,7}*448, {8,2,2,7}*448, {2,2,2,28}*448, {2,2,4,14}*448, {2,4,2,14}*448, {4,2,2,14}*448
   5-fold covers : {2,10,2,7}*560, {10,2,2,7}*560, {2,2,2,35}*560
   6-fold covers : {2,12,2,7}*672, {12,2,2,7}*672, {4,6,2,7}*672a, {6,4,2,7}*672a, {2,4,2,21}*672, {4,2,2,21}*672, {2,2,6,14}*672, {2,6,2,14}*672, {6,2,2,14}*672, {2,2,2,42}*672
   7-fold covers : {2,2,2,49}*784, {2,2,14,7}*784, {2,14,2,7}*784, {14,2,2,7}*784
   8-fold covers : {4,8,2,7}*896a, {8,4,2,7}*896a, {4,8,2,7}*896b, {8,4,2,7}*896b, {4,4,2,7}*896, {2,16,2,7}*896, {16,2,2,7}*896, {2,2,4,28}*896, {2,4,2,28}*896, {4,2,2,28}*896, {2,4,4,14}*896, {4,4,2,14}*896, {4,2,4,14}*896, {2,2,2,56}*896, {2,2,8,14}*896, {2,8,2,14}*896, {8,2,2,14}*896
   9-fold covers : {2,18,2,7}*1008, {18,2,2,7}*1008, {2,2,2,63}*1008, {6,6,2,7}*1008a, {6,6,2,7}*1008b, {6,6,2,7}*1008c, {2,2,6,21}*1008, {2,6,2,21}*1008, {6,2,2,21}*1008
   10-fold covers : {2,20,2,7}*1120, {20,2,2,7}*1120, {4,10,2,7}*1120, {10,4,2,7}*1120, {2,4,2,35}*1120, {4,2,2,35}*1120, {2,2,10,14}*1120, {2,10,2,14}*1120, {10,2,2,14}*1120, {2,2,2,70}*1120
   11-fold covers : {2,22,2,7}*1232, {22,2,2,7}*1232, {2,2,2,77}*1232
   12-fold covers : {4,12,2,7}*1344a, {12,4,2,7}*1344a, {2,24,2,7}*1344, {24,2,2,7}*1344, {6,8,2,7}*1344, {8,6,2,7}*1344, {4,4,2,21}*1344, {2,8,2,21}*1344, {8,2,2,21}*1344, {2,2,12,14}*1344, {2,12,2,14}*1344, {12,2,2,14}*1344, {2,2,6,28}*1344a, {2,6,2,28}*1344, {6,2,2,28}*1344, {2,4,6,14}*1344a, {2,6,4,14}*1344, {4,2,6,14}*1344, {4,6,2,14}*1344a, {6,2,4,14}*1344, {6,4,2,14}*1344a, {2,2,2,84}*1344, {2,2,4,42}*1344a, {2,4,2,42}*1344, {4,2,2,42}*1344, {2,2,6,21}*1344, {4,6,2,7}*1344, {6,4,2,7}*1344, {6,6,2,7}*1344, {2,2,4,21}*1344
   13-fold covers : {2,26,2,7}*1456, {26,2,2,7}*1456, {2,2,2,91}*1456
   14-fold covers : {2,4,2,49}*1568, {4,2,2,49}*1568, {2,2,2,98}*1568, {2,28,2,7}*1568, {28,2,2,7}*1568, {4,2,14,7}*1568, {4,14,2,7}*1568, {14,4,2,7}*1568, {2,4,14,7}*1568, {2,2,14,14}*1568a, {2,2,14,14}*1568b, {2,14,2,14}*1568, {14,2,2,14}*1568
   15-fold covers : {6,10,2,7}*1680, {10,6,2,7}*1680, {2,30,2,7}*1680, {30,2,2,7}*1680, {2,10,2,21}*1680, {10,2,2,21}*1680, {2,6,2,35}*1680, {6,2,2,35}*1680, {2,2,2,105}*1680
   16-fold covers : {4,8,2,7}*1792a, {8,4,2,7}*1792a, {8,8,2,7}*1792a, {8,8,2,7}*1792b, {8,8,2,7}*1792c, {8,8,2,7}*1792d, {4,16,2,7}*1792a, {16,4,2,7}*1792a, {4,16,2,7}*1792b, {16,4,2,7}*1792b, {4,4,2,7}*1792, {4,8,2,7}*1792b, {8,4,2,7}*1792b, {2,32,2,7}*1792, {32,2,2,7}*1792, {4,4,4,14}*1792, {2,4,4,28}*1792, {4,4,2,28}*1792, {4,2,4,28}*1792, {2,4,8,14}*1792a, {2,8,4,14}*1792a, {4,8,2,14}*1792a, {8,4,2,14}*1792a, {2,2,8,28}*1792a, {2,2,4,56}*1792a, {2,4,8,14}*1792b, {2,8,4,14}*1792b, {4,8,2,14}*1792b, {8,4,2,14}*1792b, {2,2,8,28}*1792b, {2,2,4,56}*1792b, {2,4,4,14}*1792, {4,4,2,14}*1792, {2,2,4,28}*1792, {4,2,8,14}*1792, {8,2,4,14}*1792, {2,8,2,28}*1792, {8,2,2,28}*1792, {2,4,2,56}*1792, {4,2,2,56}*1792, {2,2,16,14}*1792, {2,16,2,14}*1792, {16,2,2,14}*1792, {2,2,2,112}*1792
   17-fold covers : {2,34,2,7}*1904, {34,2,2,7}*1904, {2,2,2,119}*1904
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);;
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, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope