Polytope of Type {6,12,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,3,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 5
Schlafli Type : {6,12,3,2}
Number of vertices, edges, etc : 10, 80, 40, 5, 2
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {3,12,3,2}*960, {6,6,3,2}*960
   4-fold quotients : {3,6,3,2}*480, {6,3,3,2}*480
   8-fold quotients : {3,3,3,2}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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 := ( 1, 2)( 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 := ( 3, 4)( 7,10)( 8, 9)(11,13)(12,14)(15,28)(16,27)(17,29)(18,30)(19,21)
(20,22)(23,39)(24,40)(25,42)(26,41)(31,37)(32,38)(33,36)(34,35);;
s4 := (43,44);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
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(44)!( 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(44)!( 1, 2)( 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(44)!( 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(44)!( 3, 4)( 7,10)( 8, 9)(11,13)(12,14)(15,28)(16,27)(17,29)(18,30)
(19,21)(20,22)(23,39)(24,40)(25,42)(26,41)(31,37)(32,38)(33,36)(34,35);
s4 := Sym(44)!(43,44);
poly := sub<Sym(44)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
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 >;

to this polytope