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

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

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

to this polytope