Polytope of Type {2,8,10,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,10,2,2}*1280
if this polytope has a name.
Group : SmallGroup(1280,1083341)
Rank : 6
Schlafli Type : {2,8,10,2,2}
Number of vertices, edges, etc : 2, 8, 40, 10, 2, 2
Order of s₀s₁s₂s₃s₄s₅ : 40
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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 : {2,4,10,2,2}*640
   4-fold quotients : {2,2,10,2,2}*320
   5-fold quotients : {2,8,2,2,2}*256
   8-fold quotients : {2,2,5,2,2}*160
   10-fold quotients : {2,4,2,2,2}*128
   20-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (13,18)(14,19)(15,20)(16,21)(17,22)(23,38)(24,39)(25,40)(26,41)(27,42)
(28,33)(29,34)(30,35)(31,36)(32,37);;
s2 := ( 3,23)( 4,27)( 5,26)( 6,25)( 7,24)( 8,28)( 9,32)(10,31)(11,30)(12,29)
(13,38)(14,42)(15,41)(16,40)(17,39)(18,33)(19,37)(20,36)(21,35)(22,34);;
s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)
(28,29)(30,32)(33,34)(35,37)(38,39)(40,42);;
s4 := (43,44);;
s5 := (45,46);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)!(1,2);
s1 := Sym(46)!(13,18)(14,19)(15,20)(16,21)(17,22)(23,38)(24,39)(25,40)(26,41)
(27,42)(28,33)(29,34)(30,35)(31,36)(32,37);
s2 := Sym(46)!( 3,23)( 4,27)( 5,26)( 6,25)( 7,24)( 8,28)( 9,32)(10,31)(11,30)
(12,29)(13,38)(14,42)(15,41)(16,40)(17,39)(18,33)(19,37)(20,36)(21,35)(22,34);
s3 := Sym(46)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)
(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42);
s4 := Sym(46)!(43,44);
s5 := Sym(46)!(45,46);
poly := sub<Sym(46)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope