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Polytope of Type {12,8,2}

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

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