Polytope of Type {2,6,2,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,2,12}*576
if this polytope has a name.
Group : SmallGroup(576,8545)
Rank : 5
Schlafli Type : {2,6,2,12}
Number of vertices, edges, etc : 2, 6, 6, 12, 12
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,2,12,2} of size 1152
Vertex Figure Of :
   {2,2,6,2,12} of size 1152
   {3,2,6,2,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,2,12}*288, {2,6,2,6}*288
   3-fold quotients : {2,2,2,12}*192, {2,6,2,4}*192
   4-fold quotients : {2,3,2,6}*144, {2,6,2,3}*144
   6-fold quotients : {2,3,2,4}*96, {2,2,2,6}*96, {2,6,2,2}*96
   8-fold quotients : {2,3,2,3}*72
   9-fold quotients : {2,2,2,4}*64
   12-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,4,12}*1152, {4,6,2,12}*1152a, {2,12,2,12}*1152, {2,6,2,24}*1152
   3-fold covers : {2,18,2,12}*1728, {2,6,2,36}*1728, {2,6,6,12}*1728a, {2,6,6,12}*1728b, {2,6,6,12}*1728c, {6,6,2,12}*1728a, {6,6,2,12}*1728b, {2,6,6,12}*1728e
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
s3 := (10,11)(12,13)(15,18)(16,17)(19,20);;
s4 := ( 9,15)(10,12)(11,19)(13,16)(14,17)(18,20);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(20)!(1,2);
s1 := Sym(20)!(5,6)(7,8);
s2 := Sym(20)!(3,7)(4,5)(6,8);
s3 := Sym(20)!(10,11)(12,13)(15,18)(16,17)(19,20);
s4 := Sym(20)!( 9,15)(10,12)(11,19)(13,16)(14,17)(18,20);
poly := sub<Sym(20)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope