Questions?
See the FAQ
or other info.

Polytope of Type {2,4,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,2}*384
if this polytope has a name.
Group : SmallGroup(384,20162)
Rank : 5
Schlafli Type : {2,4,6,2}
Number of vertices, edges, etc : 2, 8, 24, 12, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,6,2,2} of size 768
   {2,4,6,2,3} of size 1152
   {2,4,6,2,5} of size 1920
Vertex Figure Of :
   {2,2,4,6,2} of size 768
   {3,2,4,6,2} of size 1152
   {5,2,4,6,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,3,2}*192, {2,4,6,2}*192b, {2,4,6,2}*192c
   4-fold quotients : {2,4,3,2}*96, {2,2,6,2}*96
   8-fold quotients : {2,2,3,2}*48
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,12,2}*768b, {2,4,6,2}*768b, {2,4,6,4}*768b, {2,4,12,2}*768c, {4,4,6,2}*768d, {2,8,6,2}*768b, {2,8,6,2}*768c
   3-fold covers : {2,4,18,2}*1152, {2,4,6,6}*1152a, {2,4,6,6}*1152b, {2,12,6,2}*1152a, {2,12,6,2}*1152b, {6,4,6,2}*1152a
   5-fold covers : {2,4,6,10}*1920a, {2,20,6,2}*1920a, {10,4,6,2}*1920, {2,4,30,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 8)( 4, 6)( 5,12)( 7, 9)(10,14)(11,13)(15,18)(16,17);;
s2 := ( 6,10)( 8,13)( 9,15)(12,17);;
s3 := ( 3, 5)( 4, 7)( 6, 9)( 8,12)(10,16)(11,15)(13,18)(14,17);;
s4 := (19,20);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(20)!(1,2);
s1 := Sym(20)!( 3, 8)( 4, 6)( 5,12)( 7, 9)(10,14)(11,13)(15,18)(16,17);
s2 := Sym(20)!( 6,10)( 8,13)( 9,15)(12,17);
s3 := Sym(20)!( 3, 5)( 4, 7)( 6, 9)( 8,12)(10,16)(11,15)(13,18)(14,17);
s4 := Sym(20)!(19,20);
poly := sub<Sym(20)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

to this polytope