Polytope of Type {6,2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,12,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,134264)
Rank : 5
Schlafli Type : {6,2,12,4}
Number of vertices, edges, etc : 6, 6, 12, 24, 4
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,12,4}*576a, {6,2,12,2}*576, {6,2,6,4}*576a
   3-fold quotients : {2,2,12,4}*384a, {6,2,4,4}*384
   4-fold quotients : {3,2,12,2}*288, {3,2,6,4}*288a, {6,2,6,2}*288
   6-fold quotients : {3,2,4,4}*192, {2,2,12,2}*192, {2,2,6,4}*192a, {6,2,2,4}*192, {6,2,4,2}*192
   8-fold quotients : {3,2,6,2}*144, {6,2,3,2}*144
   9-fold quotients : {2,2,4,4}*128
   12-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96, {2,2,6,2}*96, {6,2,2,2}*96
   16-fold quotients : {3,2,3,2}*72
   18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   24-fold quotients : {2,2,3,2}*48, {3,2,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,16)(14,18)(15,17)(21,26)(22,25)(23,24)(27,28)(29,30);;
s3 := ( 7,14)( 8,10)( 9,23)(11,15)(12,29)(13,17)(16,27)(18,24)(19,25)(20,21)
(22,30)(26,28);;
s4 := ( 8,12)( 9,16)(14,21)(15,22)(17,25)(18,26);;
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*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, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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(30)!(3,4)(5,6);
s1 := Sym(30)!(1,5)(2,3)(4,6);
s2 := Sym(30)!( 8, 9)(10,11)(12,16)(14,18)(15,17)(21,26)(22,25)(23,24)(27,28)
(29,30);
s3 := Sym(30)!( 7,14)( 8,10)( 9,23)(11,15)(12,29)(13,17)(16,27)(18,24)(19,25)
(20,21)(22,30)(26,28);
s4 := Sym(30)!( 8,12)( 9,16)(14,21)(15,22)(17,25)(18,26);
poly := sub<Sym(30)|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*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, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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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