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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,2,4}*640
if this polytope has a name.
Group : SmallGroup(640,20602)
Rank : 5
Schlafli Type : {4,10,2,4}
Number of vertices, edges, etc : 4, 20, 10, 4, 4
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,10,2,4,2} of size 1280
   {4,10,2,4,3} of size 1920
Vertex Figure Of :
   {2,4,10,2,4} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,10,2,4}*320, {4,10,2,2}*320
   4-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
   5-fold quotients : {4,2,2,4}*128
   8-fold quotients : {2,5,2,2}*80
   10-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   20-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,10,4,4}*1280, {4,20,2,4}*1280, {4,10,2,8}*1280, {8,10,2,4}*1280
   3-fold covers : {4,30,2,4}*1920a, {4,10,6,4}*1920a, {4,10,2,12}*1920, {12,10,2,4}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(24)!( 2, 5)( 6,11)( 7,12)(13,17)(14,18);
s1 := Sym(24)!( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,16)(12,15)(17,20)
(18,19);
s2 := Sym(24)!( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)(10,15)(12,17)(16,19);
s3 := Sym(24)!(22,23);
s4 := Sym(24)!(21,22)(23,24);
poly := sub<Sym(24)|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*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope