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Polytope of Type {4,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6}*768a
Also Known As : {{4,4|4},{4,6|2}}. if this polytope has another name.
Group : SmallGroup(768,323566)
Rank : 4
Schlafli Type : {4,4,6}
Number of vertices, edges, etc : 16, 32, 48, 6
Order of s₀s₁s₂s₃ : 24
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) :
   2-fold quotients : {4,4,6}*384a
   3-fold quotients : {4,4,2}*256
   4-fold quotients : {4,4,6}*192
   6-fold quotients : {4,4,2}*128
   8-fold quotients : {2,4,6}*96a, {4,2,6}*96
   12-fold quotients : {4,4,2}*64
   16-fold quotients : {4,2,3}*48, {2,2,6}*48
   24-fold quotients : {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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