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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,10}*320
if this polytope has a name.
Group : SmallGroup(320,1612)
Rank : 5
Schlafli Type : {2,2,4,10}
Number of vertices, edges, etc : 2, 2, 4, 20, 10
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,10,2} of size 640
   {2,2,4,10,4} of size 1280
   {2,2,4,10,5} of size 1600
   {2,2,4,10,6} of size 1920
   {2,2,4,10,3} of size 1920
   {2,2,4,10,5} of size 1920
Vertex Figure Of :
   {2,2,2,4,10} of size 640
   {3,2,2,4,10} of size 960
   {4,2,2,4,10} of size 1280
   {5,2,2,4,10} of size 1600
   {6,2,2,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,10}*160
   4-fold quotients : {2,2,2,5}*80
   5-fold quotients : {2,2,4,2}*64
   10-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,4,20}*640, {2,4,4,10}*640, {4,2,4,10}*640, {2,2,8,10}*640
   3-fold covers : {2,2,12,10}*960, {2,6,4,10}*960, {6,2,4,10}*960, {2,2,4,30}*960a
   4-fold covers : {4,4,4,10}*1280, {2,4,4,20}*1280, {4,2,4,20}*1280, {2,4,8,10}*1280a, {2,8,4,10}*1280a, {2,2,8,20}*1280a, {2,2,4,40}*1280a, {2,4,8,10}*1280b, {2,8,4,10}*1280b, {2,2,8,20}*1280b, {2,2,4,40}*1280b, {2,4,4,10}*1280, {2,2,4,20}*1280, {4,2,8,10}*1280, {8,2,4,10}*1280, {2,2,16,10}*1280
   5-fold covers : {2,2,4,50}*1600, {2,2,20,10}*1600a, {2,10,4,10}*1600, {10,2,4,10}*1600, {2,2,20,10}*1600c
   6-fold covers : {2,4,4,30}*1920, {2,2,4,60}*1920a, {6,4,4,10}*1920, {2,4,12,10}*1920a, {2,12,4,10}*1920, {2,6,4,20}*1920, {6,2,4,20}*1920, {2,2,12,20}*1920, {4,2,4,30}*1920a, {4,6,4,10}*1920a, {4,2,12,10}*1920, {12,2,4,10}*1920, {2,2,8,30}*1920, {2,6,8,10}*1920, {6,2,8,10}*1920, {2,2,24,10}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope