Polytope of Type {4,2,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,40}*640
if this polytope has a name.
Group : SmallGroup(640,13245)
Rank : 4
Schlafli Type : {4,2,40}
Number of vertices, edges, etc : 4, 4, 40, 40
Order of s₀s₁s₂s₃ : 40
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,40,2} of size 1280
Vertex Figure Of :
   {2,4,2,40} of size 1280
   {3,4,2,40} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,20}*320, {2,2,40}*320
   4-fold quotients : {2,2,20}*160, {4,2,10}*160
   5-fold quotients : {4,2,8}*128
   8-fold quotients : {4,2,5}*80, {2,2,10}*80
   10-fold quotients : {4,2,4}*64, {2,2,8}*64
   16-fold quotients : {2,2,5}*40
   20-fold quotients : {2,2,4}*32, {4,2,2}*32
   40-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,40}*1280, {4,4,40}*1280a, {4,2,80}*1280
   3-fold covers : {4,2,120}*1920, {4,6,40}*1920a, {12,2,40}*1920
Permutation Representation (GAP) :

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