Polytope of Type {3,12,2,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,2,2,5}*1920
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 6
Schlafli Type : {3,12,2,2,5}
Number of vertices, edges, etc : 4, 24, 16, 2, 5, 5
Order of s₀s₁s₂s₃s₄s₅ : 40
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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 : {3,6,2,2,5}*960
   4-fold quotients : {3,3,2,2,5}*480
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)
(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)
(39,40);;
s1 := ( 1, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)(15,40)
(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)(34,35)
(37,38);;
s2 := ( 1,44)( 2,39)( 3,40)( 4,33)( 5,47)( 6,12)( 7,11)( 8,46)( 9,21)(10,41)
(13,24)(14,42)(15,30)(16,29)(17,28)(18,27)(19,34)(20,43)(22,31)(23,45)(25,36)
(26,48)(32,38)(35,37);;
s3 := (49,50);;
s4 := (52,53)(54,55);;
s5 := (51,52)(53,54);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(55)!( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)
(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)
(36,48)(39,40);
s1 := Sym(55)!( 1, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)
(15,40)(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)
(34,35)(37,38);
s2 := Sym(55)!( 1,44)( 2,39)( 3,40)( 4,33)( 5,47)( 6,12)( 7,11)( 8,46)( 9,21)
(10,41)(13,24)(14,42)(15,30)(16,29)(17,28)(18,27)(19,34)(20,43)(22,31)(23,45)
(25,36)(26,48)(32,38)(35,37);
s3 := Sym(55)!(49,50);
s4 := Sym(55)!(52,53)(54,55);
s5 := Sym(55)!(51,52)(53,54);
poly := sub<Sym(55)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;

to this polytope