Polytope of Type {12,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,3,2}*192
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 4
Schlafli Type : {12,3,2}
Number of vertices, edges, etc : 16, 24, 4, 2
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,3,2,2} of size 384
   {12,3,2,3} of size 576
   {12,3,2,4} of size 768
   {12,3,2,5} of size 960
   {12,3,2,6} of size 1152
   {12,3,2,7} of size 1344
   {12,3,2,9} of size 1728
   {12,3,2,10} of size 1920
Vertex Figure Of :
   {2,12,3,2} of size 384
   {4,12,3,2} of size 768
   {3,12,3,2} of size 960
   {6,12,3,2} of size 1152
   {10,12,3,2} of size 1920
   {6,12,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,3,2}*96
   4-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6,2}*384b
   3-fold covers : {12,3,2}*576
   4-fold covers : {12,3,2}*768, {12,3,4}*768a, {12,12,2}*768b, {12,6,2}*768, {12,12,2}*768c, {12,6,4}*768b
   5-fold covers : {12,15,2}*960
   6-fold covers : {12,6,2}*1152c, {12,6,6}*1152c, {12,6,2}*1152d
   7-fold covers : {12,21,2}*1344
   9-fold covers : {12,9,2}*1728, {12,3,2}*1728, {12,3,6}*1728
   10-fold covers : {12,30,2}*1920a, {12,6,10}*1920b, {60,6,2}*1920b
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)
(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)
(39,40);;
s1 := ( 1, 9)( 2, 4)( 3,25)( 5,10)( 6,48)( 7,47)( 8,13)(11,42)(12,41)(14,26)
(15,46)(16,44)(17,36)(18,33)(19,32)(20,34)(21,30)(22,35)(23,31)(24,29)(27,40)
(28,39)(37,43)(38,45);;
s2 := ( 1,46)( 2,40)( 3,39)( 4,36)( 5,48)( 6,11)( 7,12)( 8,44)( 9,24)(10,42)
(13,21)(14,41)(15,29)(16,30)(17,27)(18,28)(19,31)(20,45)(22,34)(23,43)(25,33)
(26,47)(32,37)(35,38);;
s3 := (49,50);;
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, 
s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(50)!( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)
(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)
(36,48)(39,40);
s1 := Sym(50)!( 1, 9)( 2, 4)( 3,25)( 5,10)( 6,48)( 7,47)( 8,13)(11,42)(12,41)
(14,26)(15,46)(16,44)(17,36)(18,33)(19,32)(20,34)(21,30)(22,35)(23,31)(24,29)
(27,40)(28,39)(37,43)(38,45);
s2 := Sym(50)!( 1,46)( 2,40)( 3,39)( 4,36)( 5,48)( 6,11)( 7,12)( 8,44)( 9,24)
(10,42)(13,21)(14,41)(15,29)(16,30)(17,27)(18,28)(19,31)(20,45)(22,34)(23,43)
(25,33)(26,47)(32,37)(35,38);
s3 := Sym(50)!(49,50);
poly := sub<Sym(50)|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, s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >;

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