Polytope of Type {2,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,3}*192
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 4
Schlafli Type : {2,12,3}
Number of vertices, edges, etc : 2, 16, 24, 4
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,3,2} of size 384
Vertex Figure Of :
   {2,2,12,3} of size 384
   {3,2,12,3} of size 576
   {4,2,12,3} of size 768
   {5,2,12,3} of size 960
   {6,2,12,3} of size 1152
   {7,2,12,3} of size 1344
   {9,2,12,3} of size 1728
   {10,2,12,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,3}*96
   4-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,3}*384, {2,12,6}*384b
   3-fold covers : {2,12,3}*576, {6,12,3}*576
   4-fold covers : {2,12,3}*768, {4,12,3}*768a, {8,12,3}*768, {2,12,12}*768b, {4,12,6}*768b, {2,12,6}*768, {2,12,12}*768c
   5-fold covers : {2,12,15}*960, {10,12,3}*960
   6-fold covers : {12,12,3}*1152, {4,12,3}*1152b, {2,12,6}*1152c, {6,12,6}*1152c, {2,12,6}*1152d
   7-fold covers : {2,12,21}*1344, {14,12,3}*1344
   9-fold covers : {2,12,9}*1728, {18,12,3}*1728, {2,12,3}*1728, {6,12,3}*1728
   10-fold covers : {20,12,3}*1920, {4,12,15}*1920, {2,12,30}*1920a, {10,12,6}*1920b, {2,60,6}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope