Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 120, 360, 24
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 24
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,6}*720b
   3-fold quotients : {10,6}*480a
   6-fold quotients : {5,6}*240a
   12-fold quotients : {5,6}*120a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope