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Polytope of Type {2,8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,12}*384b
if this polytope has a name.
Group : SmallGroup(384,11560)
Rank : 4
Schlafli Type : {2,8,12}
Number of vertices, edges, etc : 2, 8, 48, 12
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,12,2} of size 768
Vertex Figure Of :
   {2,2,8,12} of size 768
   {3,2,8,12} of size 1152
   {5,2,8,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,12}*192a
   3-fold quotients : {2,8,4}*128b
   4-fold quotients : {2,2,12}*96, {2,4,6}*96a
   6-fold quotients : {2,4,4}*64
   8-fold quotients : {2,2,6}*48
   12-fold quotients : {2,2,4}*32, {2,4,2}*32
   16-fold quotients : {2,2,3}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,8,12}*768a, {2,8,24}*768b, {2,8,24}*768d, {4,8,12}*768c
   3-fold covers : {2,8,36}*1152b, {6,8,12}*1152b, {2,24,12}*1152d, {2,24,12}*1152f
   5-fold covers : {2,8,60}*1920b, {10,8,12}*1920b, {2,40,12}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,24)(10,25)(11,26)(12,21)
(13,22)(14,23);;
s2 := ( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(15,21)(16,23)(17,22)(18,24)(19,26)
(20,25);;
s3 := ( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)(23,26);;
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, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(26)!(1,2);
s1 := Sym(26)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,24)(10,25)(11,26)
(12,21)(13,22)(14,23);
s2 := Sym(26)!( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(15,21)(16,23)(17,22)(18,24)
(19,26)(20,25);
s3 := Sym(26)!( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)
(23,26);
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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