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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4,2}*384c
if this polytope has a name.
Group : SmallGroup(384,20049)
Rank : 5
Schlafli Type : {2,12,4,2}
Number of vertices, edges, etc : 2, 12, 24, 4, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,4,2,2} of size 768
   {2,12,4,2,3} of size 1152
   {2,12,4,2,5} of size 1920
Vertex Figure Of :
   {2,2,12,4,2} of size 768
   {3,2,12,4,2} of size 1152
   {5,2,12,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,4,2}*192c
   4-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,4,2}*768c, {2,12,4,2}*768b
   3-fold covers : {2,36,4,2}*1152c, {6,12,4,2}*1152e, {6,12,4,2}*1152g
   5-fold covers : {10,12,4,2}*1920c, {2,60,4,2}*1920c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)(20,36)
(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)(41,50)
(44,47);;
s2 := ( 3,10)( 4, 6)( 5,21)( 7,11)( 8,45)( 9,13)(12,36)(14,22)(15,50)(16,44)
(17,28)(18,27)(19,31)(20,25)(23,46)(24,35)(26,40)(29,49)(30,41)(32,39)(33,38)
(34,43)(37,47)(42,48);;
s3 := ( 3,49)( 4,47)( 5,44)( 6,50)( 7,41)( 8,39)( 9,35)(10,46)(11,33)(12,26)
(13,45)(14,28)(15,31)(16,40)(17,48)(18,23)(19,37)(20,22)(21,36)(24,32)(25,42)
(27,29)(30,43)(34,38);;
s4 := (51,52);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(52)!(1,2);
s1 := Sym(52)!( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)
(20,36)(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)
(41,50)(44,47);
s2 := Sym(52)!( 3,10)( 4, 6)( 5,21)( 7,11)( 8,45)( 9,13)(12,36)(14,22)(15,50)
(16,44)(17,28)(18,27)(19,31)(20,25)(23,46)(24,35)(26,40)(29,49)(30,41)(32,39)
(33,38)(34,43)(37,47)(42,48);
s3 := Sym(52)!( 3,49)( 4,47)( 5,44)( 6,50)( 7,41)( 8,39)( 9,35)(10,46)(11,33)
(12,26)(13,45)(14,28)(15,31)(16,40)(17,48)(18,23)(19,37)(20,22)(21,36)(24,32)
(25,42)(27,29)(30,43)(34,38);
s4 := Sym(52)!(51,52);
poly := sub<Sym(52)|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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 >; 
 

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