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Polytope of Type {6,2,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,48}*1152
if this polytope has a name.
Group : SmallGroup(1152,133451)
Rank : 4
Schlafli Type : {6,2,48}
Number of vertices, edges, etc : 6, 6, 48, 48
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 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 : {3,2,48}*576, {6,2,24}*576
   3-fold quotients : {2,2,48}*384, {6,2,16}*384
   4-fold quotients : {3,2,24}*288, {6,2,12}*288
   6-fold quotients : {3,2,16}*192, {2,2,24}*192, {6,2,8}*192
   8-fold quotients : {3,2,12}*144, {6,2,6}*144
   9-fold quotients : {2,2,16}*128
   12-fold quotients : {3,2,8}*96, {2,2,12}*96, {6,2,4}*96
   16-fold quotients : {3,2,6}*72, {6,2,3}*72
   18-fold quotients : {2,2,8}*64
   24-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
   32-fold quotients : {3,2,3}*36
   36-fold quotients : {2,2,4}*32
   48-fold quotients : {2,2,3}*24, {3,2,2}*24
   72-fold quotients : {2,2,2}*16
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)(24,27)(25,29)
(26,28)(30,33)(31,35)(32,34)(36,39)(37,41)(38,40)(42,45)(43,47)(44,46)(49,52)
(50,51)(53,54);;
s3 := ( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,31)(23,26)
(24,28)(27,37)(29,32)(30,34)(33,43)(35,38)(36,40)(39,49)(41,44)(42,46)(45,53)
(47,50)(48,51)(52,54);;
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*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(54)!(3,4)(5,6);
s1 := Sym(54)!(1,5)(2,3)(4,6);
s2 := Sym(54)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(24,27)
(25,29)(26,28)(30,33)(31,35)(32,34)(36,39)(37,41)(38,40)(42,45)(43,47)(44,46)
(49,52)(50,51)(53,54);
s3 := Sym(54)!( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,31)
(23,26)(24,28)(27,37)(29,32)(30,34)(33,43)(35,38)(36,40)(39,49)(41,44)(42,46)
(45,53)(47,50)(48,51)(52,54);
poly := sub<Sym(54)|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*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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