Polytope of Type {10,4,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,2,3}*480
if this polytope has a name.
Group : SmallGroup(480,1097)
Rank : 5
Schlafli Type : {10,4,2,3}
Number of vertices, edges, etc : 10, 20, 4, 3, 3
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,4,2,3,2} of size 960
   {10,4,2,3,3} of size 1920
   {10,4,2,3,4} of size 1920
Vertex Figure Of :
   {2,10,4,2,3} of size 960
   {4,10,4,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,2,2,3}*240
   4-fold quotients : {5,2,2,3}*120
   5-fold quotients : {2,4,2,3}*96
   10-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,4,2,3}*960, {10,8,2,3}*960, {10,4,2,6}*960
   3-fold covers : {10,4,2,9}*1440, {10,12,2,3}*1440, {10,4,6,3}*1440, {30,4,2,3}*1440a
   4-fold covers : {20,8,2,3}*1920a, {40,4,2,3}*1920a, {20,8,2,3}*1920b, {40,4,2,3}*1920b, {20,4,2,3}*1920, {10,16,2,3}*1920, {10,4,4,6}*1920, {20,4,2,6}*1920, {10,4,2,12}*1920, {10,8,2,6}*1920, {10,4,4,3}*1920b
Permutation Representation (GAP) :

s0 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,17)(10,15)(12,13)(14,18)(16,19);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,15)(12,16)(17,19)(18,20);;
s3 := (22,23);;
s4 := (21,22);;
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, 
s3*s4*s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
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(23)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20);
s1 := Sym(23)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,17)(10,15)(12,13)(14,18)(16,19);
s2 := Sym(23)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,15)(12,16)(17,19)
(18,20);
s3 := Sym(23)!(22,23);
s4 := Sym(23)!(21,22);
poly := sub<Sym(23)|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, s3*s4*s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, 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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