Polytope of Type {3,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,8,6}*1152
Also Known As : {{3,8}₆,{8,6|2}}. if this polytope has another name.
Group : SmallGroup(1152,155791)
Rank : 4
Schlafli Type : {3,8,6}
Number of vertices, edges, etc : 12, 48, 96, 6
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {3,8,2}*384
   4-fold quotients : {3,4,6}*288
   12-fold quotients : {3,4,2}*96
   16-fold quotients : {3,2,6}*72
   24-fold quotients : {3,4,2}*48
   32-fold quotients : {3,2,3}*36
   48-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(19,20)(21,22)(25,29)(26,30)
(27,32)(28,31)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47);;
s1 := ( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(18,20)(21,30)(22,31)(23,32)
(24,29)(26,28)(34,36)(37,46)(38,47)(39,48)(40,45)(42,44);;
s2 := ( 1, 7)( 2, 8)( 3, 5)( 4, 6)( 9,13)(10,14)(11,15)(12,16)(17,39)(18,40)
(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,45)(26,46)(27,47)(28,48)(29,41)
(30,42)(31,43)(32,44);;
s3 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)
(11,27)(12,28)(13,29)(14,30)(15,31)(16,32);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(48)!( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(19,20)(21,22)(25,29)
(26,30)(27,32)(28,31)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47);
s1 := Sym(48)!( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(18,20)(21,30)(22,31)
(23,32)(24,29)(26,28)(34,36)(37,46)(38,47)(39,48)(40,45)(42,44);
s2 := Sym(48)!( 1, 7)( 2, 8)( 3, 5)( 4, 6)( 9,13)(10,14)(11,15)(12,16)(17,39)
(18,40)(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,45)(26,46)(27,47)(28,48)
(29,41)(30,42)(31,43)(32,44);
s3 := Sym(48)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)
(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32);
poly := sub<Sym(48)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
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