Polytope of Type {4,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,7}*112
if this polytope has a name.
Group : SmallGroup(112,31)
Rank : 4
Schlafli Type : {4,2,7}
Number of vertices, edges, etc : 4, 4, 7, 7
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,7,2} of size 224
   {4,2,7,14} of size 1568
Vertex Figure Of :
   {2,4,2,7} of size 224
   {3,4,2,7} of size 336
   {4,4,2,7} of size 448
   {6,4,2,7} of size 672
   {3,4,2,7} of size 672
   {6,4,2,7} of size 672
   {6,4,2,7} of size 672
   {8,4,2,7} of size 896
   {8,4,2,7} of size 896
   {4,4,2,7} of size 896
   {9,4,2,7} of size 1008
   {4,4,2,7} of size 1008
   {6,4,2,7} of size 1008
   {10,4,2,7} of size 1120
   {12,4,2,7} of size 1344
   {12,4,2,7} of size 1344
   {12,4,2,7} of size 1344
   {6,4,2,7} of size 1344
   {14,4,2,7} of size 1568
   {5,4,2,7} of size 1680
   {6,4,2,7} of size 1680
   {15,4,2,7} of size 1680
   {8,4,2,7} of size 1792
   {16,4,2,7} of size 1792
   {16,4,2,7} of size 1792
   {4,4,2,7} of size 1792
   {8,4,2,7} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,7}*224, {4,2,14}*224
   3-fold covers : {12,2,7}*336, {4,2,21}*336
   4-fold covers : {16,2,7}*448, {4,2,28}*448, {4,4,14}*448, {8,2,14}*448
   5-fold covers : {20,2,7}*560, {4,2,35}*560
   6-fold covers : {24,2,7}*672, {8,2,21}*672, {12,2,14}*672, {4,6,14}*672a, {4,2,42}*672
   7-fold covers : {4,2,49}*784, {28,2,7}*784, {4,14,7}*784
   8-fold covers : {32,2,7}*896, {4,4,28}*896, {4,2,56}*896, {8,2,28}*896, {4,8,14}*896a, {8,4,14}*896a, {4,8,14}*896b, {8,4,14}*896b, {4,4,14}*896, {16,2,14}*896
   9-fold covers : {36,2,7}*1008, {4,2,63}*1008, {12,2,21}*1008, {4,6,21}*1008
   10-fold covers : {40,2,7}*1120, {8,2,35}*1120, {20,2,14}*1120, {4,10,14}*1120, {4,2,70}*1120
   11-fold covers : {44,2,7}*1232, {4,2,77}*1232
   12-fold covers : {48,2,7}*1344, {16,2,21}*1344, {12,2,28}*1344, {4,6,28}*1344a, {4,12,14}*1344a, {12,4,14}*1344, {24,2,14}*1344, {8,6,14}*1344, {4,2,84}*1344, {4,4,42}*1344, {8,2,42}*1344, {4,6,21}*1344, {4,4,21}*1344b
   13-fold covers : {52,2,7}*1456, {4,2,91}*1456
   14-fold covers : {8,2,49}*1568, {4,2,98}*1568, {56,2,7}*1568, {8,14,7}*1568, {28,2,14}*1568, {4,14,14}*1568a, {4,14,14}*1568c
   15-fold covers : {60,2,7}*1680, {20,2,21}*1680, {12,2,35}*1680, {4,2,105}*1680
   16-fold covers : {64,2,7}*1792, {4,8,14}*1792a, {8,4,14}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {8,8,14}*1792c, {8,8,14}*1792d, {8,2,56}*1792, {8,4,28}*1792a, {4,4,56}*1792a, {8,4,28}*1792b, {4,4,56}*1792b, {4,8,28}*1792a, {4,4,28}*1792a, {4,4,28}*1792b, {4,8,28}*1792b, {4,8,28}*1792c, {4,8,28}*1792d, {4,16,14}*1792a, {16,4,14}*1792a, {4,16,14}*1792b, {16,4,14}*1792b, {4,4,14}*1792, {4,8,14}*1792b, {8,4,14}*1792b, {16,2,28}*1792, {4,2,112}*1792, {32,2,14}*1792
   17-fold covers : {68,2,7}*1904, {4,2,119}*1904
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,11);;
s3 := ( 5, 6)( 7, 8)( 9,10);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(11)!(2,3);
s1 := Sym(11)!(1,2)(3,4);
s2 := Sym(11)!( 6, 7)( 8, 9)(10,11);
s3 := Sym(11)!( 5, 6)( 7, 8)( 9,10);
poly := sub<Sym(11)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope