Polytope of Type {2,2,2,4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,4,30}*1920a
if this polytope has a name.
Group : SmallGroup(1920,236171)
Rank : 6
Schlafli Type : {2,2,2,4,30}
Number of vertices, edges, etc : 2, 2, 2, 4, 60, 30
Order of s₀s₁s₂s₃s₄s₅ : 60
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 : {2,2,2,2,30}*960
   3-fold quotients : {2,2,2,4,10}*640
   4-fold quotients : {2,2,2,2,15}*480
   5-fold quotients : {2,2,2,4,6}*384a
   6-fold quotients : {2,2,2,2,10}*320
   10-fold quotients : {2,2,2,2,6}*192
   12-fold quotients : {2,2,2,2,5}*160
   15-fold quotients : {2,2,2,4,2}*128
   20-fold quotients : {2,2,2,2,3}*96
   30-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)
(47,62)(48,63)(49,64)(50,65)(51,66);;
s4 := ( 7,37)( 8,41)( 9,40)(10,39)(11,38)(12,47)(13,51)(14,50)(15,49)(16,48)
(17,42)(18,46)(19,45)(20,44)(21,43)(22,52)(23,56)(24,55)(25,54)(26,53)(27,62)
(28,66)(29,65)(30,64)(31,63)(32,57)(33,61)(34,60)(35,59)(36,58);;
s5 := ( 7,13)( 8,12)( 9,16)(10,15)(11,14)(17,18)(19,21)(22,28)(23,27)(24,31)
(25,30)(26,29)(32,33)(34,36)(37,43)(38,42)(39,46)(40,45)(41,44)(47,48)(49,51)
(52,58)(53,57)(54,61)(55,60)(56,59)(62,63)(64,66);;
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!(1,2);
s1 := Sym(66)!(3,4);
s2 := Sym(66)!(5,6);
s3 := Sym(66)!(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)
(46,61)(47,62)(48,63)(49,64)(50,65)(51,66);
s4 := Sym(66)!( 7,37)( 8,41)( 9,40)(10,39)(11,38)(12,47)(13,51)(14,50)(15,49)
(16,48)(17,42)(18,46)(19,45)(20,44)(21,43)(22,52)(23,56)(24,55)(25,54)(26,53)
(27,62)(28,66)(29,65)(30,64)(31,63)(32,57)(33,61)(34,60)(35,59)(36,58);
s5 := Sym(66)!( 7,13)( 8,12)( 9,16)(10,15)(11,14)(17,18)(19,21)(22,28)(23,27)
(24,31)(25,30)(26,29)(32,33)(34,36)(37,43)(38,42)(39,46)(40,45)(41,44)(47,48)
(49,51)(52,58)(53,57)(54,61)(55,60)(56,59)(62,63)(64,66);
poly := sub<Sym(66)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope