Polytope of Type {9,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,7}*252
if this polytope has a name.
Group : SmallGroup(252,8)
Rank : 4
Schlafli Type : {9,2,7}
Number of vertices, edges, etc : 9, 9, 7, 7
Order of s₀s₁s₂s₃ : 63
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,7,2} of size 504
Vertex Figure Of :
   {2,9,2,7} of size 504
   {4,9,2,7} of size 1008
   {6,9,2,7} of size 1512
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,7}*84
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,14}*504, {18,2,7}*504
   3-fold covers : {27,2,7}*756, {9,2,21}*756
   4-fold covers : {36,2,7}*1008, {9,2,28}*1008, {18,2,14}*1008
   5-fold covers : {45,2,7}*1260, {9,2,35}*1260
   6-fold covers : {27,2,14}*1512, {54,2,7}*1512, {9,6,14}*1512, {9,2,42}*1512, {18,2,21}*1512
   7-fold covers : {9,2,49}*1764, {63,2,7}*1764
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,16);;
s3 := (10,11)(12,13)(14,15);;
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*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(16)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(16)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(16)!(11,12)(13,14)(15,16);
s3 := Sym(16)!(10,11)(12,13)(14,15);
poly := sub<Sym(16)|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*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope