Polytope of Type {2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4}*192a
if this polytope has a name.
Group : SmallGroup(192,1046)
Rank : 4
Schlafli Type : {2,12,4}
Number of vertices, edges, etc : 2, 12, 24, 4
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,4,2} of size 384
   {2,12,4,4} of size 768
   {2,12,4,6} of size 1152
   {2,12,4,3} of size 1152
   {2,12,4,6} of size 1728
   {2,12,4,10} of size 1920
Vertex Figure Of :
   {2,2,12,4} of size 384
   {3,2,12,4} of size 576
   {4,2,12,4} of size 768
   {5,2,12,4} of size 960
   {6,2,12,4} of size 1152
   {7,2,12,4} of size 1344
   {9,2,12,4} of size 1728
   {10,2,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,2}*96, {2,6,4}*96a
   3-fold quotients : {2,4,4}*64
   4-fold quotients : {2,6,2}*48
   6-fold quotients : {2,2,4}*32, {2,4,2}*32
   8-fold quotients : {2,3,2}*24
   12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,4}*384a, {2,24,4}*384a, {2,12,4}*384a, {2,24,4}*384b, {2,12,8}*384a, {2,12,8}*384b
   3-fold covers : {2,36,4}*576a, {6,12,4}*576a, {6,12,4}*576b, {2,12,12}*576a, {2,12,12}*576c
   4-fold covers : {2,12,8}*768a, {2,24,4}*768a, {2,24,8}*768a, {2,24,8}*768b, {2,24,8}*768c, {2,24,8}*768d, {4,12,8}*768a, {8,12,4}*768a, {4,12,8}*768b, {8,12,4}*768b, {4,24,4}*768a, {4,12,4}*768a, {4,12,4}*768b, {4,24,4}*768b, {4,24,4}*768c, {4,24,4}*768d, {2,12,16}*768a, {2,48,4}*768a, {2,12,16}*768b, {2,48,4}*768b, {2,12,4}*768a, {2,24,4}*768b, {2,12,8}*768b, {4,12,4}*768f, {2,12,4}*768d
   5-fold covers : {10,12,4}*960a, {2,12,20}*960, {2,60,4}*960a
   6-fold covers : {4,36,4}*1152a, {4,12,12}*1152a, {4,12,12}*1152b, {12,12,4}*1152a, {12,12,4}*1152b, {2,36,8}*1152a, {2,72,4}*1152a, {6,12,8}*1152a, {6,12,8}*1152b, {6,24,4}*1152b, {6,24,4}*1152c, {2,12,24}*1152a, {2,24,12}*1152a, {2,24,12}*1152b, {2,12,24}*1152c, {2,36,8}*1152b, {2,72,4}*1152b, {6,12,8}*1152d, {6,12,8}*1152e, {6,24,4}*1152e, {6,24,4}*1152f, {2,12,24}*1152d, {2,24,12}*1152d, {2,24,12}*1152e, {2,12,24}*1152f, {2,36,4}*1152a, {6,12,4}*1152a, {6,12,4}*1152b, {2,12,12}*1152a, {2,12,12}*1152c
   7-fold covers : {14,12,4}*1344a, {2,12,28}*1344, {2,84,4}*1344a
   9-fold covers : {2,108,4}*1728a, {18,12,4}*1728a, {6,36,4}*1728a, {6,36,4}*1728b, {6,12,4}*1728a, {6,12,4}*1728b, {2,12,36}*1728a, {2,36,12}*1728a, {2,36,12}*1728b, {2,12,12}*1728a, {2,12,12}*1728c, {6,12,12}*1728b, {6,12,12}*1728d, {6,12,12}*1728e, {6,12,12}*1728f, {2,12,12}*1728h, {6,12,4}*1728j, {2,12,4}*1728c, {2,12,4}*1728d, {6,12,4}*1728q, {2,12,12}*1728k
   10-fold covers : {4,60,4}*1920a, {4,12,20}*1920a, {20,12,4}*1920a, {2,60,8}*1920a, {2,120,4}*1920a, {10,12,8}*1920a, {10,24,4}*1920a, {2,12,40}*1920a, {2,24,20}*1920a, {2,60,8}*1920b, {2,120,4}*1920b, {10,12,8}*1920b, {10,24,4}*1920b, {2,12,40}*1920b, {2,24,20}*1920b, {2,60,4}*1920a, {10,12,4}*1920a, {2,12,20}*1920a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,12)(10,14)(11,13)(17,22)(18,21)(19,20)(23,24)(25,26);;
s2 := ( 3,10)( 4, 6)( 5,19)( 7,11)( 8,25)( 9,13)(12,23)(14,20)(15,21)(16,17)
(18,26)(22,24);;
s3 := ( 4, 8)( 5,12)(10,17)(11,18)(13,21)(14,22);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(26)!(1,2);
s1 := Sym(26)!( 4, 5)( 6, 7)( 8,12)(10,14)(11,13)(17,22)(18,21)(19,20)(23,24)
(25,26);
s2 := Sym(26)!( 3,10)( 4, 6)( 5,19)( 7,11)( 8,25)( 9,13)(12,23)(14,20)(15,21)
(16,17)(18,26)(22,24);
s3 := Sym(26)!( 4, 8)( 5,12)(10,17)(11,18)(13,21)(14,22);
poly := sub<Sym(26)|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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope