Polytope of Type {9,2,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,12,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,30201)
Rank : 5
Schlafli Type : {9,2,12,3}
Number of vertices, edges, etc : 9, 9, 16, 24, 4
Order of s₀s₁s₂s₃s₄ : 72
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 : {9,2,6,3}*864
   3-fold quotients : {3,2,12,3}*576
   4-fold quotients : {9,2,3,3}*432
   6-fold quotients : {3,2,6,3}*288
   12-fold quotients : {3,2,3,3}*144
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 := (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);;
s3 := (10,18)(11,13)(12,34)(14,19)(15,57)(16,56)(17,22)(20,51)(21,50)(23,35)
(24,55)(25,53)(26,45)(27,42)(28,41)(29,43)(30,39)(31,44)(32,40)(33,38)(36,49)
(37,48)(46,52)(47,54);;
s4 := (10,55)(11,49)(12,48)(13,45)(14,57)(15,20)(16,21)(17,53)(18,33)(19,51)
(22,30)(23,50)(24,38)(25,39)(26,36)(27,37)(28,40)(29,54)(31,43)(32,52)(34,42)
(35,56)(41,46)(44,47);;
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, s4*s2*s3*s2*s3*s2*s3*s4*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)!(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);
s3 := Sym(57)!(10,18)(11,13)(12,34)(14,19)(15,57)(16,56)(17,22)(20,51)(21,50)
(23,35)(24,55)(25,53)(26,45)(27,42)(28,41)(29,43)(30,39)(31,44)(32,40)(33,38)
(36,49)(37,48)(46,52)(47,54);
s4 := Sym(57)!(10,55)(11,49)(12,48)(13,45)(14,57)(15,20)(16,21)(17,53)(18,33)
(19,51)(22,30)(23,50)(24,38)(25,39)(26,36)(27,37)(28,40)(29,54)(31,43)(32,52)
(34,42)(35,56)(41,46)(44,47);
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, 
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope