Polytope of Type {4,2,40,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,40,2}*1280
if this polytope has a name.
Group : SmallGroup(1280,1044763)
Rank : 5
Schlafli Type : {4,2,40,2}
Number of vertices, edges, etc : 4, 4, 40, 40, 2
Order of s₀s₁s₂s₃s₄ : 40
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 : {4,2,20,2}*640, {2,2,40,2}*640
   4-fold quotients : {2,2,20,2}*320, {4,2,10,2}*320
   5-fold quotients : {4,2,8,2}*256
   8-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   10-fold quotients : {4,2,4,2}*128, {2,2,8,2}*128
   16-fold quotients : {2,2,5,2}*80
   20-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,25)(20,24)(21,27)
(22,26)(29,34)(30,33)(31,36)(32,35)(37,38)(39,42)(40,41)(43,44);;
s3 := ( 5,11)( 6, 8)( 7,19)( 9,21)(10,14)(12,16)(13,29)(15,31)(17,22)(18,24)
(20,26)(23,37)(25,39)(27,32)(28,33)(30,35)(34,43)(36,40)(38,41)(42,44);;
s4 := (45,46);;
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, 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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(46)!(2,3);
s1 := Sym(46)!(1,2)(3,4);
s2 := Sym(46)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,25)(20,24)
(21,27)(22,26)(29,34)(30,33)(31,36)(32,35)(37,38)(39,42)(40,41)(43,44);
s3 := Sym(46)!( 5,11)( 6, 8)( 7,19)( 9,21)(10,14)(12,16)(13,29)(15,31)(17,22)
(18,24)(20,26)(23,37)(25,39)(27,32)(28,33)(30,35)(34,43)(36,40)(38,41)(42,44);
s4 := Sym(46)!(45,46);
poly := sub<Sym(46)|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, 
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 >;

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