Polytope of Type {10,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240507)
Rank : 4
Schlafli Type : {10,12,4}
Number of vertices, edges, etc : 20, 120, 48, 4
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-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 : {10,6,4}*960a, {10,12,2}*960a
   4-fold quotients : {5,6,4}*480a, {10,6,2}*480a
   8-fold quotients : {5,6,2}*240a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope