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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,6,10}*1440
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 5
Schlafli Type : {6,2,6,10}
Number of vertices, edges, etc : 6, 6, 6, 30, 10
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {3,2,6,10}*720
   3-fold quotients : {2,2,6,10}*480, {6,2,2,10}*480
   5-fold quotients : {6,2,6,2}*288
   6-fold quotients : {3,2,2,10}*240, {6,2,2,5}*240
   9-fold quotients : {2,2,2,10}*160
   10-fold quotients : {3,2,6,2}*144, {6,2,3,2}*144
   12-fold quotients : {3,2,2,5}*120
   15-fold quotients : {2,2,6,2}*96, {6,2,2,2}*96
   18-fold quotients : {2,2,2,5}*80
   20-fold quotients : {3,2,3,2}*72
   30-fold quotients : {2,2,3,2}*48, {3,2,2,2}*48
   45-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 9,10)(13,14)(17,19)(18,20)(23,25)(24,26)(29,31)(30,32)(33,35)(34,36);;
s3 := ( 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);;
s4 := ( 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]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(36)!(3,4)(5,6);
s1 := Sym(36)!(1,5)(2,3)(4,6);
s2 := Sym(36)!( 9,10)(13,14)(17,19)(18,20)(23,25)(24,26)(29,31)(30,32)(33,35)
(34,36);
s3 := 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);
s4 := 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>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, 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, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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