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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,10,2}*960
if this polytope has a name.
Group : SmallGroup(960,11387)
Rank : 6
Schlafli Type : {2,2,6,10,2}
Number of vertices, edges, etc : 2, 2, 6, 30, 10, 2
Order of s₀s₁s₂s₃s₄s₅ : 30
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,6,10,2,2} of size 1920
Vertex Figure Of :
   {2,2,2,6,10,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,2,10,2}*320
   5-fold quotients : {2,2,6,2,2}*192
   6-fold quotients : {2,2,2,5,2}*160
   10-fold quotients : {2,2,3,2,2}*96
   15-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,6,10,4}*1920, {2,4,6,10,2}*1920a, {4,2,6,10,2}*1920, {2,2,12,10,2}*1920, {2,2,6,20,2}*1920a
Permutation Representation (GAP) :

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