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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,10,4}*1600
if this polytope has a name.
Group : SmallGroup(1600,10169)
Rank : 5
Schlafli Type : {10,2,10,4}
Number of vertices, edges, etc : 10, 10, 10, 20, 4
Order of s₀s₁s₂s₃s₄ : 20
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 : {5,2,10,4}*800, {10,2,10,2}*800
   4-fold quotients : {5,2,10,2}*400, {10,2,5,2}*400
   5-fold quotients : {2,2,10,4}*320, {10,2,2,4}*320
   8-fold quotients : {5,2,5,2}*200
   10-fold quotients : {5,2,2,4}*160, {2,2,10,2}*160, {10,2,2,2}*160
   20-fold quotients : {2,2,5,2}*80, {5,2,2,2}*80
   25-fold quotients : {2,2,2,4}*64
   50-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 := (13,14)(16,17)(18,19)(21,22)(23,24)(25,26)(27,28)(29,30);;
s3 := (11,13)(12,21)(14,18)(15,16)(17,27)(20,25)(22,23)(24,28)(26,29);;
s4 := (11,12)(13,16)(14,17)(15,20)(18,23)(19,24)(21,25)(22,26)(27,29)(28,30);;
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, 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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(30)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(30)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(30)!(13,14)(16,17)(18,19)(21,22)(23,24)(25,26)(27,28)(29,30);
s3 := Sym(30)!(11,13)(12,21)(14,18)(15,16)(17,27)(20,25)(22,23)(24,28)(26,29);
s4 := Sym(30)!(11,12)(13,16)(14,17)(15,20)(18,23)(19,24)(21,25)(22,26)(27,29)
(28,30);
poly := sub<Sym(30)|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, 
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope