Polytope of Type {3,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,6}*960
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 4
Schlafli Type : {3,12,6}
Number of vertices, edges, etc : 5, 40, 80, 10
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 12
Special Properties :
   Universal
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,12,6,2} of size 1920
Vertex Figure Of :
   {2,3,12,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,12,3}*480, {3,6,6}*480
   4-fold quotients : {3,3,6}*240, {3,6,3}*240
   8-fold quotients : {3,3,3}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,12,12}*1920, {6,12,6}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope