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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,7,2,3}*168
if this polytope has a name.
Group : SmallGroup(168,50)
Rank : 5
Schlafli Type : {2,7,2,3}
Number of vertices, edges, etc : 2, 7, 7, 3, 3
Order of s₀s₁s₂s₃s₄ : 42
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,7,2,3,2} of size 336
   {2,7,2,3,3} of size 672
   {2,7,2,3,4} of size 672
   {2,7,2,3,6} of size 1008
   {2,7,2,3,4} of size 1344
   {2,7,2,3,6} of size 1344
   {2,7,2,3,5} of size 1680
Vertex Figure Of :
   {2,2,7,2,3} of size 336
   {3,2,7,2,3} of size 504
   {4,2,7,2,3} of size 672
   {5,2,7,2,3} of size 840
   {6,2,7,2,3} of size 1008
   {7,2,7,2,3} of size 1176
   {8,2,7,2,3} of size 1344
   {9,2,7,2,3} of size 1512
   {10,2,7,2,3} of size 1680
   {11,2,7,2,3} of size 1848
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,7,2,6}*336, {2,14,2,3}*336
   3-fold covers : {2,7,2,9}*504, {2,21,2,3}*504
   4-fold covers : {2,7,2,12}*672, {2,28,2,3}*672, {4,14,2,3}*672, {2,14,2,6}*672
   5-fold covers : {2,7,2,15}*840, {2,35,2,3}*840
   6-fold covers : {2,7,2,18}*1008, {2,14,2,9}*1008, {2,14,6,3}*1008, {6,14,2,3}*1008, {2,21,2,6}*1008, {2,42,2,3}*1008
   7-fold covers : {2,49,2,3}*1176, {14,7,2,3}*1176, {2,7,2,21}*1176
   8-fold covers : {4,28,2,3}*1344, {2,7,2,24}*1344, {2,56,2,3}*1344, {8,14,2,3}*1344, {2,14,2,12}*1344, {2,28,2,6}*1344, {2,14,4,6}*1344, {4,14,2,6}*1344, {2,14,4,3}*1344
   9-fold covers : {2,7,2,27}*1512, {2,63,2,3}*1512, {2,21,2,9}*1512, {2,21,6,3}*1512, {6,21,2,3}*1512
   10-fold covers : {10,14,2,3}*1680, {2,7,2,30}*1680, {2,14,2,15}*1680, {2,35,2,6}*1680, {2,70,2,3}*1680
   11-fold covers : {2,7,2,33}*1848, {2,77,2,3}*1848
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := (3,4)(5,6)(7,8);;
s3 := (11,12);;
s4 := (10,11);;
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, 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope