Polytope of Type {3,2,10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,10,8}*960
if this polytope has a name.
Group : SmallGroup(960,8239)
Rank : 5
Schlafli Type : {3,2,10,8}
Number of vertices, edges, etc : 3, 3, 10, 40, 8
Order of s₀s₁s₂s₃s₄ : 120
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,10,8,2} of size 1920
Vertex Figure Of :
   {2,3,2,10,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,10,4}*480
   4-fold quotients : {3,2,10,2}*240
   5-fold quotients : {3,2,2,8}*192
   8-fold quotients : {3,2,5,2}*120
   10-fold quotients : {3,2,2,4}*96
   20-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,20,8}*1920a, {3,2,10,16}*1920, {6,2,10,8}*1920
Permutation Representation (GAP) :

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

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