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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,6,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,236178)
Rank : 6
Schlafli Type : {4,2,2,6,10}
Number of vertices, edges, etc : 4, 4, 2, 6, 30, 10
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 : {4,2,2,2,10}*640
   5-fold quotients : {4,2,2,6,2}*384
   6-fold quotients : {4,2,2,2,5}*320, {2,2,2,2,10}*320
   10-fold quotients : {4,2,2,3,2}*192, {2,2,2,6,2}*192
   12-fold quotients : {2,2,2,2,5}*160
   15-fold quotients : {4,2,2,2,2}*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 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := ( 9,10)(13,14)(17,19)(18,20)(23,25)(24,26)(29,31)(30,32)(33,35)(34,36);;
s4 := ( 7, 9)( 8,13)(11,18)(12,17)(15,24)(16,23)(19,20)(21,30)(22,29)(25,26)
(27,34)(28,33)(31,32)(35,36);;
s5 := ( 7,15)( 8,11)( 9,23)(10,25)(12,27)(13,17)(14,19)(16,21)(18,33)(20,35)
(22,28)(24,29)(26,31)(30,34)(32,36);;
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*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, 
s0*s1*s0*s1*s0*s1*s0*s1, 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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(36)!(2,3);
s1 := Sym(36)!(1,2)(3,4);
s2 := Sym(36)!(5,6);
s3 := Sym(36)!( 9,10)(13,14)(17,19)(18,20)(23,25)(24,26)(29,31)(30,32)(33,35)
(34,36);
s4 := Sym(36)!( 7, 9)( 8,13)(11,18)(12,17)(15,24)(16,23)(19,20)(21,30)(22,29)
(25,26)(27,34)(28,33)(31,32)(35,36);
s5 := Sym(36)!( 7,15)( 8,11)( 9,23)(10,25)(12,27)(13,17)(14,19)(16,21)(18,33)
(20,35)(22,28)(24,29)(26,31)(30,34)(32,36);
poly := sub<Sym(36)|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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
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 >;

to this polytope