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Polytope of Type {2,8,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,3,2}*384
if this polytope has a name.
Group : SmallGroup(384,20062)
Rank : 5
Schlafli Type : {2,8,3,2}
Number of vertices, edges, etc : 2, 16, 24, 6, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,3,2,2} of size 768
   {2,8,3,2,3} of size 1152
   {2,8,3,2,5} of size 1920
Vertex Figure Of :
   {2,2,8,3,2} of size 768
   {3,2,8,3,2} of size 1152
   {5,2,8,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,3,2}*192
   4-fold quotients : {2,4,3,2}*96
   8-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,8,3,2}*768, {2,8,6,2}*768b
   3-fold covers : {2,8,9,2}*1152, {2,24,3,2}*1152, {2,8,3,6}*1152, {6,8,3,2}*1152
   5-fold covers : {10,8,3,2}*1920, {2,8,15,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,13)( 4, 9)( 5, 8)( 6,29)( 7,31)(10,14)(11,18)(12,20)(15,17)(16,19)
(21,46)(22,50)(23,45)(24,48)(25,49)(26,47)(27,30)(28,32)(33,41)(34,43)(35,39)
(36,42)(37,44)(38,40);;
s2 := ( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)(18,40)
(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)(38,50)
(41,42);;
s3 := ( 3, 7)( 4,16)( 5,12)( 8,20)( 9,19)(10,28)(11,15)(13,31)(14,32)(17,18)
(21,23)(22,44)(24,26)(25,43)(33,35)(34,49)(36,38)(37,50)(39,41)(40,42)(45,46)
(47,48);;
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, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*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(52)!(1,2);
s1 := Sym(52)!( 3,13)( 4, 9)( 5, 8)( 6,29)( 7,31)(10,14)(11,18)(12,20)(15,17)
(16,19)(21,46)(22,50)(23,45)(24,48)(25,49)(26,47)(27,30)(28,32)(33,41)(34,43)
(35,39)(36,42)(37,44)(38,40);
s2 := Sym(52)!( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)
(18,40)(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)
(38,50)(41,42);
s3 := Sym(52)!( 3, 7)( 4,16)( 5,12)( 8,20)( 9,19)(10,28)(11,15)(13,31)(14,32)
(17,18)(21,23)(22,44)(24,26)(25,43)(33,35)(34,49)(36,38)(37,50)(39,41)(40,42)
(45,46)(47,48);
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, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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