Polytope of Type {2,2,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,5}*400
if this polytope has a name.
Group : SmallGroup(400,218)
Rank : 5
Schlafli Type : {2,2,10,5}
Number of vertices, edges, etc : 2, 2, 10, 25, 5
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,10,5,2} of size 800
Vertex Figure Of :
   {2,2,2,10,5} of size 800
   {3,2,2,10,5} of size 1200
   {4,2,2,10,5} of size 1600
   {5,2,2,10,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,10,5}*800, {2,4,10,5}*800, {2,2,10,10}*800b
   3-fold covers : {2,6,10,5}*1200, {6,2,10,5}*1200, {2,2,10,15}*1200
   4-fold covers : {8,2,10,5}*1600, {2,8,10,5}*1600, {4,4,10,5}*1600, {2,2,10,20}*1600b, {4,2,10,10}*1600b, {2,2,20,10}*1600c, {2,4,10,10}*1600c
   5-fold covers : {2,2,10,25}*2000, {2,2,10,5}*2000, {2,10,10,5}*2000b, {10,2,10,5}*2000
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 8, 9)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29);;
s3 := ( 5, 8)( 6,14)( 7,11)( 9,16)(10,22)(12,24)(13,18)(15,20)(19,28)(21,25)
(23,26)(27,29);;
s4 := ( 5, 6)( 7,10)( 8,12)( 9,11)(14,19)(15,18)(16,21)(17,20)(22,23)(24,27)
(25,26)(28,29);;
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, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope