Questions?
See the FAQ
or other info.

Polytope of Type {4,12,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,2,2}*384a
if this polytope has a name.
Group : SmallGroup(384,18267)
Rank : 5
Schlafli Type : {4,12,2,2}
Number of vertices, edges, etc : 4, 24, 12, 2, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,12,2,2,2} of size 768
   {4,12,2,2,3} of size 1152
   {4,12,2,2,5} of size 1920
Vertex Figure Of :
   {2,4,12,2,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,2,2}*192, {4,6,2,2}*192a
   3-fold quotients : {4,4,2,2}*128
   4-fold quotients : {2,6,2,2}*96
   6-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   8-fold quotients : {2,3,2,2}*48
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,4,2}*768a, {4,12,2,4}*768a, {8,12,2,2}*768a, {4,24,2,2}*768a, {8,12,2,2}*768b, {4,24,2,2}*768b, {4,12,2,2}*768a
   3-fold covers : {4,36,2,2}*1152a, {4,12,2,6}*1152a, {4,12,6,2}*1152a, {4,12,6,2}*1152b, {12,12,2,2}*1152a, {12,12,2,2}*1152b
   5-fold covers : {4,60,2,2}*1920a, {4,12,2,10}*1920a, {4,12,10,2}*1920a, {20,12,2,2}*1920
Permutation Representation (GAP) :
s0 := ( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);;
s1 := ( 1, 2)( 3, 7)( 4, 9)( 5, 8)( 6,14)(10,13)(11,18)(12,17)(15,24)(16,23)
(19,22)(20,21);;
s2 := ( 1, 4)( 2,11)( 3, 8)( 6,19)( 7,17)( 9,12)(10,15)(13,21)(14,23)(16,20);;
s3 := (25,26);;
s4 := (27,28);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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(28)!( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);
s1 := Sym(28)!( 1, 2)( 3, 7)( 4, 9)( 5, 8)( 6,14)(10,13)(11,18)(12,17)(15,24)
(16,23)(19,22)(20,21);
s2 := Sym(28)!( 1, 4)( 2,11)( 3, 8)( 6,19)( 7,17)( 9,12)(10,15)(13,21)(14,23)
(16,20);
s3 := Sym(28)!(25,26);
s4 := Sym(28)!(27,28);
poly := sub<Sym(28)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
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