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Polytope of Type {6,2,8,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,8,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {6,2,8,3}
Number of vertices, edges, etc : 6, 6, 16, 24, 6
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 : {3,2,8,3}*576, {6,2,4,3}*576
   3-fold quotients : {2,2,8,3}*384
   4-fold quotients : {3,2,4,3}*288, {6,2,4,3}*288
   6-fold quotients : {2,2,4,3}*192
   8-fold quotients : {3,2,4,3}*144, {6,2,2,3}*144
   12-fold quotients : {2,2,4,3}*96
   16-fold quotients : {3,2,2,3}*72
   24-fold quotients : {2,2,2,3}*48
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 := ( 7,17)( 8,13)( 9,12)(10,33)(11,35)(14,18)(15,22)(16,24)(19,21)(20,23)
(25,50)(26,54)(27,49)(28,52)(29,53)(30,51)(31,34)(32,36)(37,45)(38,47)(39,43)
(40,46)(41,48)(42,44);;
s3 := ( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)(22,44)
(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)(42,54)
(45,46);;
s4 := ( 7,11)( 8,20)( 9,16)(12,24)(13,23)(14,32)(15,19)(17,35)(18,36)(21,22)
(25,27)(26,48)(28,30)(29,47)(37,39)(38,53)(40,42)(41,54)(43,45)(44,46)(49,50)
(51,52);;
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*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*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)!( 7,17)( 8,13)( 9,12)(10,33)(11,35)(14,18)(15,22)(16,24)(19,21)
(20,23)(25,50)(26,54)(27,49)(28,52)(29,53)(30,51)(31,34)(32,36)(37,45)(38,47)
(39,43)(40,46)(41,48)(42,44);
s3 := Sym(54)!( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)
(22,44)(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)
(42,54)(45,46);
s4 := Sym(54)!( 7,11)( 8,20)( 9,16)(12,24)(13,23)(14,32)(15,19)(17,35)(18,36)
(21,22)(25,27)(26,48)(28,30)(29,47)(37,39)(38,53)(40,42)(41,54)(43,45)(44,46)
(49,50)(51,52);
poly := sub<Sym(54)|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*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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