Polytope of Type {6,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,24}*576
if this polytope has a name.
Group : SmallGroup(576,6554)
Rank : 4
Schlafli Type : {6,2,24}
Number of vertices, edges, etc : 6, 6, 24, 24
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,24,2} of size 1152
Vertex Figure Of :
   {2,6,2,24} of size 1152
   {3,6,2,24} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,24}*288, {6,2,12}*288
   3-fold quotients : {2,2,24}*192, {6,2,8}*192
   4-fold quotients : {3,2,12}*144, {6,2,6}*144
   6-fold quotients : {3,2,8}*96, {2,2,12}*96, {6,2,4}*96
   8-fold quotients : {3,2,6}*72, {6,2,3}*72
   9-fold quotients : {2,2,8}*64
   12-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
   16-fold quotients : {3,2,3}*36
   18-fold quotients : {2,2,4}*32
   24-fold quotients : {2,2,3}*24, {3,2,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,4,24}*1152a, {12,2,24}*1152, {6,2,48}*1152
   3-fold covers : {6,2,72}*1728, {18,2,24}*1728, {6,6,24}*1728a, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728e
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);;
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, 
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(30)!(3,4)(5,6);
s1 := Sym(30)!(1,5)(2,3)(4,6);
s2 := Sym(30)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(25,28)
(26,27)(29,30);
s3 := Sym(30)!( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,29)
(23,26)(24,27)(28,30);
poly := sub<Sym(30)|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, 
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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