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Polytope of Type {4,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,12}*768a
Also Known As : {{4,4}4,{4,12|2}}. if this polytope has another name.
Group : SmallGroup(768,201148)
Rank : 4
Schlafli Type : {4,4,12}
Number of vertices, edges, etc : 8, 16, 48, 12
Order of s0s1s2s3 : 12
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 : {4,4,12}*384, {4,4,6}*384a
   3-fold quotients : {4,4,4}*256b
   4-fold quotients : {2,4,12}*192a, {4,2,12}*192, {4,4,6}*192
   6-fold quotients : {4,4,4}*128, {4,4,2}*128
   8-fold quotients : {2,2,12}*96, {2,4,6}*96a, {4,2,6}*96
   12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   16-fold quotients : {4,2,3}*48, {2,2,6}*48
   24-fold quotients : {2,2,4}*32, {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 := (13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(37,40)(38,41)(39,42)(43,46)
(44,47)(45,48);;
s1 := (25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)
(35,47)(36,48);;
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, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,32)(26,31)
(27,33)(28,35)(29,34)(30,36)(37,44)(38,43)(39,45)(40,47)(41,46)(42,48);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(48)!(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(37,40)(38,41)(39,42)
(43,46)(44,47)(45,48);
s1 := Sym(48)!(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)
(34,46)(35,47)(36,48);
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, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,32)
(26,31)(27,33)(28,35)(29,34)(30,36)(37,44)(38,43)(39,45)(40,47)(41,46)(42,48);
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*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 >; 
 
References : None.
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