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Polytope of Type {3,2,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,16}*768a
if this polytope has a name.
Group : SmallGroup(768,323301)
Rank : 5
Schlafli Type : {3,2,4,16}
Number of vertices, edges, etc : 3, 3, 4, 32, 16
Order of s0s1s2s3s4 : 48
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,4,8}*384a, {3,2,2,16}*384
   4-fold quotients : {3,2,4,4}*192, {3,2,2,8}*192
   8-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
   16-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)
(14,30)(15,31)(16,32)(17,33)(18,34)(19,35)(36,52)(37,53)(38,54)(39,55)(40,56)
(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)
(51,67);;
s3 := ( 6, 7)(10,11)(12,14)(13,15)(16,18)(17,19)(20,24)(21,25)(22,27)(23,26)
(28,34)(29,35)(30,32)(31,33)(36,44)(37,45)(38,47)(39,46)(40,48)(41,49)(42,51)
(43,50)(52,64)(53,65)(54,67)(55,66)(56,60)(57,61)(58,63)(59,62);;
s4 := ( 4,36)( 5,37)( 6,39)( 7,38)( 8,40)( 9,41)(10,43)(11,42)(12,46)(13,47)
(14,44)(15,45)(16,50)(17,51)(18,48)(19,49)(20,52)(21,53)(22,55)(23,54)(24,56)
(25,57)(26,59)(27,58)(28,62)(29,63)(30,60)(31,61)(32,66)(33,67)(34,64)
(35,65);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(67)!(2,3);
s1 := Sym(67)!(1,2);
s2 := Sym(67)!( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)
(13,29)(14,30)(15,31)(16,32)(17,33)(18,34)(19,35)(36,52)(37,53)(38,54)(39,55)
(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)
(51,67);
s3 := Sym(67)!( 6, 7)(10,11)(12,14)(13,15)(16,18)(17,19)(20,24)(21,25)(22,27)
(23,26)(28,34)(29,35)(30,32)(31,33)(36,44)(37,45)(38,47)(39,46)(40,48)(41,49)
(42,51)(43,50)(52,64)(53,65)(54,67)(55,66)(56,60)(57,61)(58,63)(59,62);
s4 := Sym(67)!( 4,36)( 5,37)( 6,39)( 7,38)( 8,40)( 9,41)(10,43)(11,42)(12,46)
(13,47)(14,44)(15,45)(16,50)(17,51)(18,48)(19,49)(20,52)(21,53)(22,55)(23,54)
(24,56)(25,57)(26,59)(27,58)(28,62)(29,63)(30,60)(31,61)(32,66)(33,67)(34,64)
(35,65);
poly := sub<Sym(67)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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