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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,3,2,3}*216
if this polytope has a name.
Group : SmallGroup(216,162)
Rank : 6
Schlafli Type : {3,2,3,2,3}
Number of vertices, edges, etc : 3, 3, 3, 3, 3, 3
Order of s₀s₁s₂s₃s₄s₅ : 3
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,3,2,3,2} of size 432
   {3,2,3,2,3,3} of size 864
   {3,2,3,2,3,4} of size 864
   {3,2,3,2,3,6} of size 1296
   {3,2,3,2,3,4} of size 1728
   {3,2,3,2,3,6} of size 1728
Vertex Figure Of :
   {2,3,2,3,2,3} of size 432
   {3,3,2,3,2,3} of size 864
   {4,3,2,3,2,3} of size 864
   {6,3,2,3,2,3} of size 1296
   {4,3,2,3,2,3} of size 1728
   {6,3,2,3,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,3,2,6}*432, {3,2,6,2,3}*432, {6,2,3,2,3}*432
   3-fold covers : {3,2,3,2,9}*648, {3,2,9,2,3}*648, {9,2,3,2,3}*648, {3,2,3,6,3}*648, {3,6,3,2,3}*648
   4-fold covers : {3,2,3,2,12}*864, {3,2,12,2,3}*864, {12,2,3,2,3}*864, {3,2,6,2,6}*864, {6,2,3,2,6}*864, {6,2,6,2,3}*864
   5-fold covers : {3,2,3,2,15}*1080, {3,2,15,2,3}*1080, {15,2,3,2,3}*1080
   6-fold covers : {3,2,3,2,18}*1296, {3,2,6,2,9}*1296, {3,2,9,2,6}*1296, {3,2,18,2,3}*1296, {6,2,3,2,9}*1296, {6,2,9,2,3}*1296, {9,2,3,2,6}*1296, {9,2,6,2,3}*1296, {18,2,3,2,3}*1296, {3,2,3,6,6}*1296a, {3,2,6,6,3}*1296a, {3,6,3,2,6}*1296, {3,6,6,2,3}*1296a, {6,2,3,6,3}*1296, {6,6,3,2,3}*1296a, {3,2,3,6,6}*1296b, {3,2,6,6,3}*1296b, {3,6,6,2,3}*1296b, {6,6,3,2,3}*1296b
   7-fold covers : {3,2,3,2,21}*1512, {3,2,21,2,3}*1512, {21,2,3,2,3}*1512
   8-fold covers : {3,2,3,2,24}*1728, {3,2,24,2,3}*1728, {24,2,3,2,3}*1728, {3,2,6,2,12}*1728, {3,2,12,2,6}*1728, {6,2,3,2,12}*1728, {6,2,12,2,3}*1728, {12,2,3,2,6}*1728, {12,2,6,2,3}*1728, {3,2,6,4,6}*1728, {6,4,6,2,3}*1728, {3,2,3,4,6}*1728, {3,2,6,4,3}*1728, {3,4,6,2,3}*1728, {6,4,3,2,3}*1728, {6,2,6,2,6}*1728
   9-fold covers : {3,2,9,2,9}*1944, {9,2,3,2,9}*1944, {9,2,9,2,3}*1944, {3,2,3,6,9}*1944, {3,2,9,6,3}*1944, {3,6,9,2,3}*1944, {9,6,3,2,3}*1944, {3,6,3,2,9}*1944, {9,2,3,6,3}*1944, {3,6,3,6,3}*1944, {3,2,3,2,27}*1944, {3,2,27,2,3}*1944, {27,2,3,2,3}*1944, {3,2,3,6,3}*1944a, {3,2,3,6,3}*1944b, {3,6,3,2,3}*1944a, {3,6,3,2,3}*1944b
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (5,6);;
s3 := (4,5);;
s4 := (8,9);;
s5 := (7,8);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(9)!(2,3);
s1 := Sym(9)!(1,2);
s2 := Sym(9)!(5,6);
s3 := Sym(9)!(4,5);
s4 := Sym(9)!(8,9);
s5 := Sym(9)!(7,8);
poly := sub<Sym(9)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5 >;

to this polytope