Polytope of Type {3,2,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,46}*552
if this polytope has a name.
Group : SmallGroup(552,34)
Rank : 4
Schlafli Type : {3,2,46}
Number of vertices, edges, etc : 3, 3, 46, 46
Order of s₀s₁s₂s₃ : 138
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,46,2} of size 1104
Vertex Figure Of :
   {2,3,2,46} of size 1104
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,23}*276
   23-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,92}*1104, {6,2,46}*1104
   3-fold covers : {9,2,46}*1656, {3,6,46}*1656, {3,2,138}*1656
Permutation Representation (GAP) :

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

to this polytope