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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,12,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 5
Schlafli Type : {2,3,12,6}
Number of vertices, edges, etc : 2, 5, 40, 80, 10
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 : {2,3,12,3}*960, {2,3,6,6}*960
   4-fold quotients : {2,3,3,6}*480, {2,3,6,3}*480
   8-fold quotients : {2,3,3,3}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 7, 8)( 9,22)(10,21)(11,23)(12,24)(13,15)(14,16)(17,39)(18,40)(19,37)
(20,38)(25,26)(29,34)(30,33)(31,36)(32,35)(41,42);;
s2 := ( 7, 8)( 9,12)(10,11)(13,24)(14,23)(15,22)(16,21)(19,20)(25,35)(26,36)
(27,34)(28,33)(31,32)(37,42)(38,41)(39,43)(40,44);;
s3 := ( 5,27)( 6,28)( 7,25)( 8,26)( 9,40)(10,39)(11,37)(12,38)(13,15)(14,16)
(17,21)(18,22)(19,23)(20,24)(29,32)(30,31)(33,36)(34,35)(43,44);;
s4 := ( 3, 4)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,29)(18,30)(19,32)(20,31)
(21,24)(22,23)(25,42)(26,41)(27,43)(28,44)(33,40)(34,39)(35,37)(36,38);;
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*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, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*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(44)!(1,2);
s1 := Sym(44)!( 7, 8)( 9,22)(10,21)(11,23)(12,24)(13,15)(14,16)(17,39)(18,40)
(19,37)(20,38)(25,26)(29,34)(30,33)(31,36)(32,35)(41,42);
s2 := Sym(44)!( 7, 8)( 9,12)(10,11)(13,24)(14,23)(15,22)(16,21)(19,20)(25,35)
(26,36)(27,34)(28,33)(31,32)(37,42)(38,41)(39,43)(40,44);
s3 := Sym(44)!( 5,27)( 6,28)( 7,25)( 8,26)( 9,40)(10,39)(11,37)(12,38)(13,15)
(14,16)(17,21)(18,22)(19,23)(20,24)(29,32)(30,31)(33,36)(34,35)(43,44);
s4 := Sym(44)!( 3, 4)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,29)(18,30)(19,32)
(20,31)(21,24)(22,23)(25,42)(26,41)(27,43)(28,44)(33,40)(34,39)(35,37)(36,38);
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*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, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*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 >;

to this polytope