Polytope of Type {8,2,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,40}*1280
if this polytope has a name.
Group : SmallGroup(1280,161916)
Rank : 4
Schlafli Type : {8,2,40}
Number of vertices, edges, etc : 8, 8, 40, 40
Order of s₀s₁s₂s₃ : 40
Order of s₀s₁s₂s₃s₂s₁ : 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 : {4,2,40}*640, {8,2,20}*640
   4-fold quotients : {4,2,20}*320, {2,2,40}*320, {8,2,10}*320
   5-fold quotients : {8,2,8}*256
   8-fold quotients : {8,2,5}*160, {2,2,20}*160, {4,2,10}*160
   10-fold quotients : {4,2,8}*128, {8,2,4}*128
   16-fold quotients : {4,2,5}*80, {2,2,10}*80
   20-fold quotients : {4,2,4}*64, {2,2,8}*64, {8,2,2}*64
   32-fold quotients : {2,2,5}*40
   40-fold quotients : {2,2,4}*32, {4,2,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,29)(24,28)(25,31)
(26,30)(33,38)(34,37)(35,40)(36,39)(41,42)(43,46)(44,45)(47,48);;
s3 := ( 9,15)(10,12)(11,23)(13,25)(14,18)(16,20)(17,33)(19,35)(21,26)(22,28)
(24,30)(27,41)(29,43)(31,36)(32,37)(34,39)(38,47)(40,44)(42,45)(46,48);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(48)!(2,3)(4,5)(6,7);
s1 := Sym(48)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(48)!(10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,29)(24,28)
(25,31)(26,30)(33,38)(34,37)(35,40)(36,39)(41,42)(43,46)(44,45)(47,48);
s3 := Sym(48)!( 9,15)(10,12)(11,23)(13,25)(14,18)(16,20)(17,33)(19,35)(21,26)
(22,28)(24,30)(27,41)(29,43)(31,36)(32,37)(34,39)(38,47)(40,44)(42,45)(46,48);
poly := sub<Sym(48)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

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