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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,10,6,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,236178)
Rank : 6
Schlafli Type : {2,4,10,6,2}
Number of vertices, edges, etc : 2, 4, 20, 30, 6, 2
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 : {2,2,10,6,2}*960
   3-fold quotients : {2,4,10,2,2}*640
   5-fold quotients : {2,4,2,6,2}*384
   6-fold quotients : {2,2,10,2,2}*320
   10-fold quotients : {2,4,2,3,2}*192, {2,2,2,6,2}*192
   12-fold quotients : {2,2,5,2,2}*160
   15-fold quotients : {2,4,2,2,2}*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 := (33,48)(34,49)(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);;
s2 := ( 3,33)( 4,37)( 5,36)( 6,35)( 7,34)( 8,38)( 9,42)(10,41)(11,40)(12,39)
(13,43)(14,47)(15,46)(16,45)(17,44)(18,48)(19,52)(20,51)(21,50)(22,49)(23,53)
(24,57)(25,56)(26,55)(27,54)(28,58)(29,62)(30,61)(31,60)(32,59);;
s3 := ( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)
(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)(42,45)
(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60);;
s4 := ( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,23)(19,24)(20,25)(21,26)(22,27)
(33,38)(34,39)(35,40)(36,41)(37,42)(48,53)(49,54)(50,55)(51,56)(52,57);;
s5 := (63,64);;
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, 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, s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope