Polytope of Type {2,2,4,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,10,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,236178)
Rank : 6
Schlafli Type : {2,2,4,10,6}
Number of vertices, edges, etc : 2, 2, 4, 20, 30, 6
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 : {2,2,2,10,6}*960
   3-fold quotients : {2,2,4,10,2}*640
   5-fold quotients : {2,2,4,2,6}*384
   6-fold quotients : {2,2,2,10,2}*320
   10-fold quotients : {2,2,4,2,3}*192, {2,2,2,2,6}*192
   12-fold quotients : {2,2,2,5,2}*160
   15-fold quotients : {2,2,4,2,2}*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 := (35,50)(36,51)(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);;
s3 := ( 5,35)( 6,39)( 7,38)( 8,37)( 9,36)(10,40)(11,44)(12,43)(13,42)(14,41)
(15,45)(16,49)(17,48)(18,47)(19,46)(20,50)(21,54)(22,53)(23,52)(24,51)(25,55)
(26,59)(27,58)(28,57)(29,56)(30,60)(31,64)(32,63)(33,62)(34,61);;
s4 := ( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)
(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)(44,47)
(50,51)(52,54)(55,61)(56,60)(57,64)(58,63)(59,62);;
s5 := ( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)(24,29)
(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59);;
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, 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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope