Polytope of Type {9,2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,12,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,30173)
Rank : 5
Schlafli Type : {9,2,12,4}
Number of vertices, edges, etc : 9, 9, 12, 24, 4
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {9,2,6,4}*864c
   3-fold quotients : {3,2,12,4}*576b
   4-fold quotients : {9,2,3,4}*432
   6-fold quotients : {3,2,6,4}*288c
   12-fold quotients : {3,2,3,4}*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)(15,25)(17,21)(18,20)(19,33)(22,38)(23,41)(24,26)(27,43)
(28,29)(30,46)(31,49)(32,39)(34,37)(35,53)(36,50)(40,52)(44,55)(45,47)(48,57)
(51,54);;
s3 := (10,17)(11,13)(12,28)(14,18)(15,52)(16,20)(19,43)(21,29)(22,57)(23,51)
(24,35)(25,34)(26,38)(27,32)(30,53)(31,42)(33,47)(36,56)(37,48)(39,46)(40,45)
(41,50)(44,54)(49,55);;
s4 := (10,42)(11,51)(12,54)(13,43)(14,27)(15,25)(16,56)(17,52)(18,35)(19,38)
(20,53)(21,40)(22,33)(23,26)(24,41)(28,57)(29,48)(30,46)(31,34)(32,50)(36,39)
(37,49)(44,47)(45,55);;
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*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)(15,25)(17,21)(18,20)(19,33)(22,38)(23,41)(24,26)
(27,43)(28,29)(30,46)(31,49)(32,39)(34,37)(35,53)(36,50)(40,52)(44,55)(45,47)
(48,57)(51,54);
s3 := Sym(57)!(10,17)(11,13)(12,28)(14,18)(15,52)(16,20)(19,43)(21,29)(22,57)
(23,51)(24,35)(25,34)(26,38)(27,32)(30,53)(31,42)(33,47)(36,56)(37,48)(39,46)
(40,45)(41,50)(44,54)(49,55);
s4 := Sym(57)!(10,42)(11,51)(12,54)(13,43)(14,27)(15,25)(16,56)(17,52)(18,35)
(19,38)(20,53)(21,40)(22,33)(23,26)(24,41)(28,57)(29,48)(30,46)(31,34)(32,50)
(36,39)(37,49)(44,47)(45,55);
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*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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