Polytope of Type {10,2,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,40}*1600
if this polytope has a name.
Group : SmallGroup(1600,8115)
Rank : 4
Schlafli Type : {10,2,40}
Number of vertices, edges, etc : 10, 10, 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 : {5,2,40}*800, {10,2,20}*800
   4-fold quotients : {5,2,20}*400, {10,2,10}*400
   5-fold quotients : {2,2,40}*320, {10,2,8}*320
   8-fold quotients : {5,2,10}*200, {10,2,5}*200
   10-fold quotients : {5,2,8}*160, {2,2,20}*160, {10,2,4}*160
   16-fold quotients : {5,2,5}*100
   20-fold quotients : {5,2,4}*80, {2,2,10}*80, {10,2,2}*80
   25-fold quotients : {2,2,8}*64
   40-fold quotients : {2,2,5}*40, {5,2,2}*40
   50-fold quotients : {2,2,4}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (12,13)(14,15)(16,19)(17,21)(18,20)(22,23)(24,29)(25,31)(26,30)(27,33)
(28,32)(35,40)(36,39)(37,42)(38,41)(43,44)(45,48)(46,47)(49,50);;
s3 := (11,17)(12,14)(13,25)(15,27)(16,20)(18,22)(19,35)(21,37)(23,28)(24,30)
(26,32)(29,43)(31,45)(33,38)(34,39)(36,41)(40,49)(42,46)(44,47)(48,50);;
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*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(50)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(50)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(50)!(12,13)(14,15)(16,19)(17,21)(18,20)(22,23)(24,29)(25,31)(26,30)
(27,33)(28,32)(35,40)(36,39)(37,42)(38,41)(43,44)(45,48)(46,47)(49,50);
s3 := Sym(50)!(11,17)(12,14)(13,25)(15,27)(16,20)(18,22)(19,35)(21,37)(23,28)
(24,30)(26,32)(29,43)(31,45)(33,38)(34,39)(36,41)(40,49)(42,46)(44,47)(48,50);
poly := sub<Sym(50)|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*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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