Polytope of Type {9,2,8,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,8,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,30201)
Rank : 5
Schlafli Type : {9,2,8,3}
Number of vertices, edges, etc : 9, 9, 16, 24, 6
Order of s₀s₁s₂s₃s₄ : 36
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 : {9,2,4,3}*864
   3-fold quotients : {3,2,8,3}*576
   4-fold quotients : {9,2,4,3}*432
   6-fold quotients : {3,2,4,3}*288
   8-fold quotients : {9,2,2,3}*216
   12-fold quotients : {3,2,4,3}*144
   24-fold quotients : {3,2,2,3}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,20)(11,16)(12,15)(13,36)(14,38)(17,21)(18,25)(19,27)(22,24)(23,26)
(28,53)(29,57)(30,52)(31,55)(32,56)(33,54)(34,37)(35,39)(40,48)(41,50)(42,46)
(43,49)(44,51)(45,47);;
s3 := (11,12)(13,14)(15,28)(16,31)(18,23)(19,22)(20,40)(21,43)(24,46)(25,47)
(26,32)(27,29)(30,51)(33,50)(34,35)(36,52)(37,54)(38,41)(39,44)(42,56)(45,57)
(48,49);;
s4 := (10,14)(11,23)(12,19)(15,27)(16,26)(17,35)(18,22)(20,38)(21,39)(24,25)
(28,30)(29,51)(31,33)(32,50)(40,42)(41,56)(43,45)(44,57)(46,48)(47,49)(52,53)
(54,55);;
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, 
s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(57)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(57)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(57)!(10,20)(11,16)(12,15)(13,36)(14,38)(17,21)(18,25)(19,27)(22,24)
(23,26)(28,53)(29,57)(30,52)(31,55)(32,56)(33,54)(34,37)(35,39)(40,48)(41,50)
(42,46)(43,49)(44,51)(45,47);
s3 := Sym(57)!(11,12)(13,14)(15,28)(16,31)(18,23)(19,22)(20,40)(21,43)(24,46)
(25,47)(26,32)(27,29)(30,51)(33,50)(34,35)(36,52)(37,54)(38,41)(39,44)(42,56)
(45,57)(48,49);
s4 := Sym(57)!(10,14)(11,23)(12,19)(15,27)(16,26)(17,35)(18,22)(20,38)(21,39)
(24,25)(28,30)(29,51)(31,33)(32,50)(40,42)(41,56)(43,45)(44,57)(46,48)(47,49)
(52,53)(54,55);
poly := sub<Sym(57)|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, s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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