Polytope of Type {3,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,2}*192
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 4
Schlafli Type : {3,12,2}
Number of vertices, edges, etc : 4, 24, 16, 2
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,12,2,2} of size 384
   {3,12,2,3} of size 576
   {3,12,2,4} of size 768
   {3,12,2,5} of size 960
   {3,12,2,6} of size 1152
   {3,12,2,7} of size 1344
   {3,12,2,9} of size 1728
   {3,12,2,10} of size 1920
Vertex Figure Of :
   {2,3,12,2} of size 384
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,2}*96
   4-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,12,4}*384, {6,12,2}*384b
   3-fold covers : {3,12,2}*576, {3,12,6}*576
   4-fold covers : {3,12,2}*768, {3,12,4}*768a, {3,12,8}*768, {12,12,2}*768b, {6,12,4}*768b, {6,12,2}*768, {12,12,2}*768d
   5-fold covers : {15,12,2}*960, {3,12,10}*960
   6-fold covers : {3,12,12}*1152, {3,12,4}*1152b, {6,12,2}*1152c, {6,12,6}*1152d, {6,12,2}*1152d
   7-fold covers : {21,12,2}*1344, {3,12,14}*1344
   9-fold covers : {9,12,2}*1728, {3,12,18}*1728, {3,12,2}*1728, {3,12,6}*1728
   10-fold covers : {3,12,20}*1920, {15,12,4}*1920, {30,12,2}*1920a, {6,12,10}*1920b, {6,60,2}*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, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)(15,40)
(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)(34,35)
(37,38);;
s2 := ( 1,44)( 2,39)( 3,40)( 4,33)( 5,47)( 6,12)( 7,11)( 8,46)( 9,21)(10,41)
(13,24)(14,42)(15,30)(16,29)(17,28)(18,27)(19,34)(20,43)(22,31)(23,45)(25,36)
(26,48)(32,38)(35,37);;
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, 
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)
(15,40)(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)
(34,35)(37,38);
s2 := Sym(50)!( 1,44)( 2,39)( 3,40)( 4,33)( 5,47)( 6,12)( 7,11)( 8,46)( 9,21)
(10,41)(13,24)(14,42)(15,30)(16,29)(17,28)(18,27)(19,34)(20,43)(22,31)(23,45)
(25,36)(26,48)(32,38)(35,37);
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, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;

to this polytope