Polytope of Type {9,2,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,12}*432
if this polytope has a name.
Group : SmallGroup(432,292)
Rank : 4
Schlafli Type : {9,2,12}
Number of vertices, edges, etc : 9, 9, 12, 12
Order of s₀s₁s₂s₃ : 36
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,12,2} of size 864
   {9,2,12,4} of size 1728
   {9,2,12,4} of size 1728
   {9,2,12,4} of size 1728
   {9,2,12,3} of size 1728
Vertex Figure Of :
   {2,9,2,12} of size 864
   {4,9,2,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,2,6}*216
   3-fold quotients : {9,2,4}*144, {3,2,12}*144
   4-fold quotients : {9,2,3}*108
   6-fold quotients : {9,2,2}*72, {3,2,6}*72
   9-fold quotients : {3,2,4}*48
   12-fold quotients : {3,2,3}*36
   18-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,24}*864, {18,2,12}*864
   3-fold covers : {9,2,36}*1296, {9,6,12}*1296a, {27,2,12}*1296, {9,6,12}*1296b
   4-fold covers : {9,2,48}*1728, {36,2,12}*1728, {18,4,12}*1728, {18,2,24}*1728, {9,4,12}*1728
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)(16,19)(17,18)(20,21);;
s3 := (10,16)(11,13)(12,20)(14,17)(15,18)(19,21);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(21)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(21)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(21)!(11,12)(13,14)(16,19)(17,18)(20,21);
s3 := Sym(21)!(10,16)(11,13)(12,20)(14,17)(15,18)(19,21);
poly := sub<Sym(21)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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