Polytope of Type {3,2,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,40}*480
if this polytope has a name.
Group : SmallGroup(480,328)
Rank : 4
Schlafli Type : {3,2,40}
Number of vertices, edges, etc : 3, 3, 40, 40
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,40,2} of size 960
   {3,2,40,4} of size 1920
   {3,2,40,4} of size 1920
Vertex Figure Of :
   {2,3,2,40} of size 960
   {3,3,2,40} of size 1920
   {4,3,2,40} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,20}*240
   4-fold quotients : {3,2,10}*120
   5-fold quotients : {3,2,8}*96
   8-fold quotients : {3,2,5}*60
   10-fold quotients : {3,2,4}*48
   20-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,80}*960, {6,2,40}*960
   3-fold covers : {9,2,40}*1440, {3,6,40}*1440, {3,2,120}*1440
   4-fold covers : {3,2,160}*1920, {6,4,40}*1920a, {12,2,40}*1920, {6,2,80}*1920, {3,4,40}*1920
Permutation Representation (GAP) :

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