Polytope of Type {12,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,4}*768a
if this polytope has a name.
Group : SmallGroup(768,201129)
Rank : 4
Schlafli Type : {12,8,4}
Number of vertices, edges, etc : 12, 48, 16, 4
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 : {12,4,4}*384
   3-fold quotients : {4,8,4}*256a
   4-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192
   6-fold quotients : {4,4,4}*128
   8-fold quotients : {12,2,2}*96, {6,2,4}*96, {6,4,2}*96a
   12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   16-fold quotients : {3,2,4}*48, {6,2,2}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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