Polytope of Type {2,40,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,40,2,5}*1600
if this polytope has a name.
Group : SmallGroup(1600,8115)
Rank : 5
Schlafli Type : {2,40,2,5}
Number of vertices, edges, etc : 2, 40, 40, 5, 5
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 : {2,20,2,5}*800
   4-fold quotients : {2,10,2,5}*400
   5-fold quotients : {2,8,2,5}*320
   8-fold quotients : {2,5,2,5}*200
   10-fold quotients : {2,4,2,5}*160
   20-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)(19,25)
(20,24)(27,32)(28,31)(29,34)(30,33)(35,36)(37,40)(38,39)(41,42);;
s2 := ( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,27)(13,29)(15,20)(16,22)
(18,24)(21,35)(23,37)(25,30)(26,31)(28,33)(32,41)(34,38)(36,39)(40,42);;
s3 := (44,45)(46,47);;
s4 := (43,44)(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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(47)!(1,2);
s1 := Sym(47)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)
(19,25)(20,24)(27,32)(28,31)(29,34)(30,33)(35,36)(37,40)(38,39)(41,42);
s2 := Sym(47)!( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,27)(13,29)(15,20)
(16,22)(18,24)(21,35)(23,37)(25,30)(26,31)(28,33)(32,41)(34,38)(36,39)(40,42);
s3 := Sym(47)!(44,45)(46,47);
s4 := Sym(47)!(43,44)(45,46);
poly := sub<Sym(47)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope