Polytope of Type {8,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240560)
Rank : 4
Schlafli Type : {8,10,6}
Number of vertices, edges, etc : 8, 80, 60, 12
Order of s₀s₁s₂s₃ : 8
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 : {4,10,6}*960a
   4-fold quotients : {2,10,6}*480b
   8-fold quotients : {2,5,6}*240a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope