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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,6}*480
if this polytope has a name.
Group : SmallGroup(480,1207)
Rank : 5
Schlafli Type : {2,2,10,6}
Number of vertices, edges, etc : 2, 2, 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 :
   {2,2,10,6,2} of size 960
   {2,2,10,6,3} of size 1440
   {2,2,10,6,4} of size 1920
   {2,2,10,6,3} of size 1920
   {2,2,10,6,4} of size 1920
Vertex Figure Of :
   {2,2,2,10,6} of size 960
   {3,2,2,10,6} of size 1440
   {4,2,2,10,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,10,2}*160
   5-fold quotients : {2,2,2,6}*96
   6-fold quotients : {2,2,5,2}*80
   10-fold quotients : {2,2,2,3}*48
   15-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,10,12}*960, {2,2,20,6}*960a, {2,4,10,6}*960, {4,2,10,6}*960
   3-fold covers : {2,2,10,18}*1440, {2,2,30,6}*1440a, {2,6,10,6}*1440, {6,2,10,6}*1440, {2,2,30,6}*1440b
   4-fold covers : {4,4,10,6}*1920, {2,4,20,6}*1920, {2,2,20,12}*1920, {4,2,10,12}*1920, {4,2,20,6}*1920a, {2,4,10,12}*1920, {2,8,10,6}*1920, {8,2,10,6}*1920, {2,2,10,24}*1920, {2,2,40,6}*1920, {2,2,20,6}*1920a
Permutation Representation (GAP) :

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

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