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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,10}*640
if this polytope has a name.
Group : SmallGroup(640,21152)
Rank : 5
Schlafli Type : {2,2,8,10}
Number of vertices, edges, etc : 2, 2, 8, 40, 10
Order of s₀s₁s₂s₃s₄ : 40
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,8,10,2} of size 1280
Vertex Figure Of :
   {2,2,2,8,10} of size 1280
   {3,2,2,8,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,4,10}*320
   4-fold quotients : {2,2,2,10}*160
   5-fold quotients : {2,2,8,2}*128
   8-fold quotients : {2,2,2,5}*80
   10-fold quotients : {2,2,4,2}*64
   20-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,8,10}*1280a, {2,2,8,20}*1280a, {4,2,8,10}*1280, {2,2,16,10}*1280
   3-fold covers : {2,2,8,30}*1920, {2,6,8,10}*1920, {6,2,8,10}*1920, {2,2,24,10}*1920
Permutation Representation (GAP) :

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