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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,10,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 5
Schlafli Type : {6,2,10,6}
Number of vertices, edges, etc : 6, 6, 10, 30, 6
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 : {3,2,10,6}*720
   3-fold quotients : {2,2,10,6}*480, {6,2,10,2}*480
   5-fold quotients : {6,2,2,6}*288
   6-fold quotients : {3,2,10,2}*240, {6,2,5,2}*240
   9-fold quotients : {2,2,10,2}*160
   10-fold quotients : {3,2,2,6}*144, {6,2,2,3}*144
   12-fold quotients : {3,2,5,2}*120
   15-fold quotients : {2,2,2,6}*96, {6,2,2,2}*96
   18-fold quotients : {2,2,5,2}*80
   20-fold quotients : {3,2,2,3}*72
   30-fold quotients : {2,2,2,3}*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 := (11,12)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)
(33,34)(35,36);;
s3 := ( 7,11)( 8,15)( 9,19)(10,17)(12,21)(13,25)(14,23)(16,27)(18,31)(20,29)
(24,35)(26,33)(30,32)(34,36);;
s4 := ( 7,13)( 8, 9)(10,14)(11,23)(12,24)(15,17)(16,18)(19,25)(20,26)(21,33)
(22,34)(27,29)(28,30)(31,35)(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, 
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(36)!(3,4)(5,6);
s1 := Sym(36)!(1,5)(2,3)(4,6);
s2 := Sym(36)!(11,12)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)
(31,32)(33,34)(35,36);
s3 := Sym(36)!( 7,11)( 8,15)( 9,19)(10,17)(12,21)(13,25)(14,23)(16,27)(18,31)
(20,29)(24,35)(26,33)(30,32)(34,36);
s4 := Sym(36)!( 7,13)( 8, 9)(10,14)(11,23)(12,24)(15,17)(16,18)(19,25)(20,26)
(21,33)(22,34)(27,29)(28,30)(31,35)(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, 
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