Polytope of Type {7,2,4}

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

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

Permutation Representation (Magma) :

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

to this polytope