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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,4,12}*1728b
if this polytope has a name.
Group : SmallGroup(1728,30173)
Rank : 5
Schlafli Type : {9,2,4,12}
Number of vertices, edges, etc : 9, 9, 4, 24, 12
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 : {9,2,4,6}*864c
   3-fold quotients : {3,2,4,12}*576b
   4-fold quotients : {9,2,4,3}*432
   6-fold quotients : {3,2,4,6}*288c
   12-fold quotients : {3,2,4,3}*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 := (10,15)(11,19)(12,22)(13,23)(14,24)(16,30)(17,31)(18,32)(20,36)(21,37)
(25,42)(26,43)(27,41)(28,44)(29,45)(33,54)(34,52)(35,50)(38,51)(39,53)(40,49)
(46,56)(47,57)(48,55);;
s3 := (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);;
s4 := (10,18)(11,14)(12,29)(13,17)(15,32)(16,21)(19,24)(20,28)(22,45)(23,31)
(25,35)(26,52)(27,38)(30,37)(33,48)(34,43)(36,44)(39,57)(40,46)(41,51)(42,50)
(47,53)(49,56)(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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(57)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(57)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(57)!(10,15)(11,19)(12,22)(13,23)(14,24)(16,30)(17,31)(18,32)(20,36)
(21,37)(25,42)(26,43)(27,41)(28,44)(29,45)(33,54)(34,52)(35,50)(38,51)(39,53)
(40,49)(46,56)(47,57)(48,55);
s3 := 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);
s4 := Sym(57)!(10,18)(11,14)(12,29)(13,17)(15,32)(16,21)(19,24)(20,28)(22,45)
(23,31)(25,35)(26,52)(27,38)(30,37)(33,48)(34,43)(36,44)(39,57)(40,46)(41,51)
(42,50)(47,53)(49,56)(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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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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