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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,10,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,236178)
Rank : 6
Schlafli Type : {2,2,6,10,4}
Number of vertices, edges, etc : 2, 2, 6, 30, 20, 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 : {2,2,6,10,2}*960
   3-fold quotients : {2,2,2,10,4}*640
   5-fold quotients : {2,2,6,2,4}*384
   6-fold quotients : {2,2,2,10,2}*320
   10-fold quotients : {2,2,3,2,4}*192, {2,2,6,2,2}*192
   12-fold quotients : {2,2,2,5,2}*160
   15-fold quotients : {2,2,2,2,4}*128
   20-fold quotients : {2,2,3,2,2}*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 := (10,15)(11,16)(12,17)(13,18)(14,19)(25,30)(26,31)(27,32)(28,33)(29,34)
(40,45)(41,46)(42,47)(43,48)(44,49)(55,60)(56,61)(57,62)(58,63)(59,64);;
s3 := ( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(16,19)(17,18)(20,25)(21,29)(22,28)
(23,27)(24,26)(31,34)(32,33)(35,40)(36,44)(37,43)(38,42)(39,41)(46,49)(47,48)
(50,55)(51,59)(52,58)(53,57)(54,56)(61,64)(62,63);;
s4 := ( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,26)(27,29)
(30,31)(32,34)(35,51)(36,50)(37,54)(38,53)(39,52)(40,56)(41,55)(42,59)(43,58)
(44,57)(45,61)(46,60)(47,64)(48,63)(49,62);;
s5 := ( 5,35)( 6,36)( 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);;
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*s4*s3*s2*s3*s4*s3, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(10,15)(11,16)(12,17)(13,18)(14,19)(25,30)(26,31)(27,32)(28,33)
(29,34)(40,45)(41,46)(42,47)(43,48)(44,49)(55,60)(56,61)(57,62)(58,63)(59,64);
s3 := Sym(64)!( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(16,19)(17,18)(20,25)(21,29)
(22,28)(23,27)(24,26)(31,34)(32,33)(35,40)(36,44)(37,43)(38,42)(39,41)(46,49)
(47,48)(50,55)(51,59)(52,58)(53,57)(54,56)(61,64)(62,63);
s4 := Sym(64)!( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,26)
(27,29)(30,31)(32,34)(35,51)(36,50)(37,54)(38,53)(39,52)(40,56)(41,55)(42,59)
(43,58)(44,57)(45,61)(46,60)(47,64)(48,63)(49,62);
s5 := Sym(64)!( 5,35)( 6,36)( 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);
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope