Polytope of Type {20,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,2,10}*800
if this polytope has a name.
Group : SmallGroup(800,1127)
Rank : 4
Schlafli Type : {20,2,10}
Number of vertices, edges, etc : 20, 20, 10, 10
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,2,10,2} of size 1600
Vertex Figure Of :
   {2,20,2,10} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,2,5}*400, {10,2,10}*400
   4-fold quotients : {5,2,10}*200, {10,2,5}*200
   5-fold quotients : {20,2,2}*160, {4,2,10}*160
   8-fold quotients : {5,2,5}*100
   10-fold quotients : {4,2,5}*80, {2,2,10}*80, {10,2,2}*80
   20-fold quotients : {2,2,5}*40, {5,2,2}*40
   25-fold quotients : {4,2,2}*32
   50-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,2,20}*1600, {20,4,10}*1600, {40,2,10}*1600
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)(18,20);;
s2 := (23,24)(25,26)(27,28)(29,30);;
s3 := (21,25)(22,23)(24,29)(26,27)(28,30);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(30)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);
s1 := Sym(30)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)
(18,20);
s2 := Sym(30)!(23,24)(25,26)(27,28)(29,30);
s3 := Sym(30)!(21,25)(22,23)(24,29)(26,27)(28,30);
poly := sub<Sym(30)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope