Polytope of Type {2,2,2,6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,6,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,236184)
Rank : 6
Schlafli Type : {2,2,2,6,20}
Number of vertices, edges, etc : 2, 2, 2, 6, 60, 20
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 : {2,2,2,6,10}*960
   3-fold quotients : {2,2,2,2,20}*640
   5-fold quotients : {2,2,2,6,4}*384a
   6-fold quotients : {2,2,2,2,10}*320
   10-fold quotients : {2,2,2,6,2}*192
   12-fold quotients : {2,2,2,2,5}*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 := (12,17)(13,18)(14,19)(15,20)(16,21)(27,32)(28,33)(29,34)(30,35)(31,36)
(42,47)(43,48)(44,49)(45,50)(46,51)(57,62)(58,63)(59,64)(60,65)(61,66);;
s4 := ( 7,12)( 8,16)( 9,15)(10,14)(11,13)(18,21)(19,20)(22,27)(23,31)(24,30)
(25,29)(26,28)(33,36)(34,35)(37,57)(38,61)(39,60)(40,59)(41,58)(42,52)(43,56)
(44,55)(45,54)(46,53)(47,62)(48,66)(49,65)(50,64)(51,63);;
s5 := ( 7,38)( 8,37)( 9,41)(10,40)(11,39)(12,43)(13,42)(14,46)(15,45)(16,44)
(17,48)(18,47)(19,51)(20,50)(21,49)(22,53)(23,52)(24,56)(25,55)(26,54)(27,58)
(28,57)(29,61)(30,60)(31,59)(32,63)(33,62)(34,66)(35,65)(36,64);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope