Polytope of Type {9,2,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,48}*1728
if this polytope has a name.
Group : SmallGroup(1728,3040)
Rank : 4
Schlafli Type : {9,2,48}
Number of vertices, edges, etc : 9, 9, 48, 48
Order of s₀s₁s₂s₃ : 144
Order of s₀s₁s₂s₃s₂s₁ : 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 : {9,2,24}*864
   3-fold quotients : {9,2,16}*576, {3,2,48}*576
   4-fold quotients : {9,2,12}*432
   6-fold quotients : {9,2,8}*288, {3,2,24}*288
   8-fold quotients : {9,2,6}*216
   9-fold quotients : {3,2,16}*192
   12-fold quotients : {9,2,4}*144, {3,2,12}*144
   16-fold quotients : {9,2,3}*108
   18-fold quotients : {3,2,8}*96
   24-fold quotients : {9,2,2}*72, {3,2,6}*72
   36-fold quotients : {3,2,4}*48
   48-fold quotients : {3,2,3}*36
   72-fold quotients : {3,2,2}*24
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)(15,18)(16,20)(17,19)(21,24)(22,26)(23,25)(27,30)(28,32)
(29,31)(33,36)(34,38)(35,37)(39,42)(40,44)(41,43)(45,48)(46,50)(47,49)(52,55)
(53,54)(56,57);;
s3 := (10,16)(11,13)(12,22)(14,17)(15,19)(18,28)(20,23)(21,25)(24,34)(26,29)
(27,31)(30,40)(32,35)(33,37)(36,46)(38,41)(39,43)(42,52)(44,47)(45,49)(48,56)
(50,53)(51,54)(55,57);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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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