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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,6,6}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 5
Schlafli Type : {10,2,6,6}
Number of vertices, edges, etc : 10, 10, 6, 18, 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 : {5,2,6,6}*720a
   3-fold quotients : {10,2,2,6}*480, {10,2,6,2}*480
   5-fold quotients : {2,2,6,6}*288a
   6-fold quotients : {5,2,2,6}*240, {5,2,6,2}*240, {10,2,2,3}*240, {10,2,3,2}*240
   9-fold quotients : {10,2,2,2}*160
   12-fold quotients : {5,2,2,3}*120, {5,2,3,2}*120
   15-fold quotients : {2,2,2,6}*96, {2,2,6,2}*96
   18-fold quotients : {5,2,2,2}*80
   30-fold quotients : {2,2,2,3}*48, {2,2,3,2}*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)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (15,16)(19,20)(21,22)(23,24)(25,26)(27,28);;
s3 := (11,15)(12,19)(13,23)(14,21)(17,27)(18,25)(22,24)(26,28);;
s4 := (11,17)(12,13)(14,18)(15,25)(16,26)(19,21)(20,22)(23,27)(24,28);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(28)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(28)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(28)!(15,16)(19,20)(21,22)(23,24)(25,26)(27,28);
s3 := Sym(28)!(11,15)(12,19)(13,23)(14,21)(17,27)(18,25)(22,24)(26,28);
s4 := Sym(28)!(11,17)(12,13)(14,18)(15,25)(16,26)(19,21)(20,22)(23,27)(24,28);
poly := sub<Sym(28)|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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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