Polytope of Type {2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12}*192c
if this polytope has a name.
Group : SmallGroup(192,1470)
Rank : 4
Schlafli Type : {2,4,12}
Number of vertices, edges, etc : 2, 4, 24, 12
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,12,2} of size 384
   {2,4,12,4} of size 768
   {2,4,12,4} of size 768
   {2,4,12,4} of size 768
   {2,4,12,6} of size 1152
   {2,4,12,6} of size 1152
   {2,4,12,10} of size 1920
Vertex Figure Of :
   {2,2,4,12} of size 384
   {3,2,4,12} of size 576
   {4,2,4,12} of size 768
   {5,2,4,12} of size 960
   {6,2,4,12} of size 1152
   {7,2,4,12} of size 1344
   {9,2,4,12} of size 1728
   {10,2,4,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,6}*96c
   4-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,12}*384b
   3-fold covers : {2,4,36}*576c
   4-fold covers : {2,4,12}*768c, {4,4,12}*768d, {2,4,12}*768d, {4,4,12}*768e, {2,8,12}*768e, {2,8,12}*768f, {2,4,24}*768c, {2,4,24}*768d
   5-fold covers : {2,4,60}*960c
   6-fold covers : {2,4,36}*1152b, {6,4,12}*1152b, {2,12,12}*1152f, {2,12,12}*1152g
   7-fold covers : {2,4,84}*1344c
   9-fold covers : {2,4,108}*1728c, {2,12,12}*1728o
   10-fold covers : {10,4,12}*1920b, {2,20,12}*1920b, {2,4,60}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope