Polytope of Type {2,3,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,12,3}*960
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 5
Schlafli Type : {2,3,12,3}
Number of vertices, edges, etc : 2, 5, 40, 40, 5
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,12,3,2} of size 1920
Vertex Figure Of :
   {2,2,3,12,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,6,3}*480
   4-fold quotients : {2,3,3,3}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,12,6}*1920, {2,6,12,3}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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