Polytope of Type {10,6,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6,2,4}*960
if this polytope has a name.
Group : SmallGroup(960,11219)
Rank : 5
Schlafli Type : {10,6,2,4}
Number of vertices, edges, etc : 10, 30, 6, 4, 4
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,6,2,4,2} of size 1920
Vertex Figure Of :
   {2,10,6,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6,2,2}*480
   3-fold quotients : {10,2,2,4}*320
   5-fold quotients : {2,6,2,4}*192
   6-fold quotients : {5,2,2,4}*160, {10,2,2,2}*160
   10-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
   12-fold quotients : {5,2,2,2}*80
   15-fold quotients : {2,2,2,4}*64
   20-fold quotients : {2,3,2,2}*48
   30-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,6,4,4}*1920, {10,12,2,4}*1920, {20,6,2,4}*1920a, {10,6,2,8}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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