Polytope of Type {3,4,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,2,7}*336
if this polytope has a name.
Group : SmallGroup(336,212)
Rank : 5
Schlafli Type : {3,4,2,7}
Number of vertices, edges, etc : 3, 6, 4, 7, 7
Order of s₀s₁s₂s₃s₄ : 21
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,4,2,7,2} of size 672
Vertex Figure Of :
   {2,3,4,2,7} of size 672
   {4,3,4,2,7} of size 1344
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,4,2,7}*672, {3,4,2,14}*672, {6,4,2,7}*672b, {6,4,2,7}*672c
   3-fold covers : {9,4,2,7}*1008, {3,4,2,21}*1008
   4-fold covers : {12,4,2,7}*1344b, {12,4,2,7}*1344c, {3,4,2,28}*1344, {3,8,2,7}*1344, {3,4,2,14}*1344, {6,4,2,7}*1344, {6,4,2,14}*1344b, {6,4,2,14}*1344c
   5-fold covers : {15,4,2,7}*1680, {3,4,2,35}*1680
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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