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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,10}*480
if this polytope has a name.
Group : SmallGroup(480,1207)
Rank : 5
Schlafli Type : {2,2,6,10}
Number of vertices, edges, etc : 2, 2, 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 :
   {2,2,6,10,2} of size 960
   {2,2,6,10,4} of size 1920
Vertex Figure Of :
   {2,2,2,6,10} of size 960
   {3,2,2,6,10} of size 1440
   {4,2,2,6,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,2,10}*160
   5-fold quotients : {2,2,6,2}*96
   6-fold quotients : {2,2,2,5}*80
   10-fold quotients : {2,2,3,2}*48
   15-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,12,10}*960, {2,2,6,20}*960a, {2,4,6,10}*960a, {4,2,6,10}*960
   3-fold covers : {2,2,18,10}*1440, {2,2,6,30}*1440a, {2,6,6,10}*1440a, {2,6,6,10}*1440b, {6,2,6,10}*1440, {2,2,6,30}*1440b
   4-fold covers : {4,4,6,10}*1920, {2,4,12,10}*1920a, {2,2,12,20}*1920, {4,2,12,10}*1920, {4,2,6,20}*1920a, {2,4,6,20}*1920a, {2,8,6,10}*1920, {8,2,6,10}*1920, {2,2,24,10}*1920, {2,2,6,40}*1920, {2,2,6,20}*1920a, {2,4,6,10}*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);;
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*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, 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(34)!(1,2);
s1 := Sym(34)!(3,4);
s2 := Sym(34)!( 7, 8)(11,12)(15,17)(16,18)(21,23)(22,24)(27,29)(28,30)(31,33)
(32,34);
s3 := Sym(34)!( 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(34)!( 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);
poly := sub<Sym(34)|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*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, 
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