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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,30,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,236171)
Rank : 6
Schlafli Type : {2,2,2,30,4}
Number of vertices, edges, etc : 2, 2, 2, 30, 60, 4
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 : {2,2,2,30,2}*960
   3-fold quotients : {2,2,2,10,4}*640
   4-fold quotients : {2,2,2,15,2}*480
   5-fold quotients : {2,2,2,6,4}*384a
   6-fold quotients : {2,2,2,10,2}*320
   10-fold quotients : {2,2,2,6,2}*192
   12-fold quotients : {2,2,2,5,2}*160
   15-fold quotients : {2,2,2,2,4}*128
   20-fold quotients : {2,2,2,3,2}*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 := ( 8,11)( 9,10)(12,17)(13,21)(14,20)(15,19)(16,18)(23,26)(24,25)(27,32)
(28,36)(29,35)(30,34)(31,33)(38,41)(39,40)(42,47)(43,51)(44,50)(45,49)(46,48)
(53,56)(54,55)(57,62)(58,66)(59,65)(60,64)(61,63);;
s4 := ( 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)(37,58)(38,57)(39,61)(40,60)(41,59)(42,53)(43,52)
(44,56)(45,55)(46,54)(47,63)(48,62)(49,66)(50,65)(51,64);;
s5 := ( 7,37)( 8,38)( 9,39)(10,40)(11,41)(12,42)(13,43)(14,44)(15,45)(16,46)
(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)
(28,58)(29,59)(30,60)(31,61)(32,62)(33,63)(34,64)(35,65)(36,66);;
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*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope