Polytope of Type {3,2,8,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8,10,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 6
Schlafli Type : {3,2,8,10,2}
Number of vertices, edges, etc : 3, 3, 8, 40, 10, 2
Order of s₀s₁s₂s₃s₄s₅ : 120
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 : {3,2,4,10,2}*960
   4-fold quotients : {3,2,2,10,2}*480
   5-fold quotients : {3,2,8,2,2}*384
   8-fold quotients : {3,2,2,5,2}*240
   10-fold quotients : {3,2,4,2,2}*192
   20-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope