Polytope of Type {6,2,24,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,24,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,152551)
Rank : 5
Schlafli Type : {6,2,24,2}
Number of vertices, edges, etc : 6, 6, 24, 24, 2
Order of s₀s₁s₂s₃s₄ : 24
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 : {3,2,24,2}*576, {6,2,12,2}*576
   3-fold quotients : {2,2,24,2}*384, {6,2,8,2}*384
   4-fold quotients : {3,2,12,2}*288, {6,2,6,2}*288
   6-fold quotients : {3,2,8,2}*192, {2,2,12,2}*192, {6,2,4,2}*192
   8-fold quotients : {3,2,6,2}*144, {6,2,3,2}*144
   9-fold quotients : {2,2,8,2}*128
   12-fold quotients : {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 : {2,2,4,2}*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)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(25,28)(26,27)
(29,30);;
s3 := ( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,29)(23,26)
(24,27)(28,30);;
s4 := (31,32);;
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, 
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*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(32)!(3,4)(5,6);
s1 := Sym(32)!(1,5)(2,3)(4,6);
s2 := Sym(32)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(25,28)
(26,27)(29,30);
s3 := Sym(32)!( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,29)
(23,26)(24,27)(28,30);
s4 := Sym(32)!(31,32);
poly := sub<Sym(32)|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, 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*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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