Polytope of Type {5,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,5}*100
if this polytope has a name.
Group : SmallGroup(100,13)
Rank : 4
Schlafli Type : {5,2,5}
Number of vertices, edges, etc : 5, 5, 5, 5
Order of s₀s₁s₂s₃ : 5
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,5,2} of size 200
   {5,2,5,3} of size 600
   {5,2,5,5} of size 600
   {5,2,5,10} of size 1000
   {5,2,5,4} of size 1200
   {5,2,5,6} of size 1200
   {5,2,5,3} of size 1200
   {5,2,5,5} of size 1200
   {5,2,5,6} of size 1200
   {5,2,5,6} of size 1200
   {5,2,5,10} of size 1200
   {5,2,5,10} of size 1200
   {5,2,5,4} of size 1600
   {5,2,5,5} of size 1600
Vertex Figure Of :
   {2,5,2,5} of size 200
   {3,5,2,5} of size 600
   {5,5,2,5} of size 600
   {10,5,2,5} of size 1000
   {4,5,2,5} of size 1200
   {6,5,2,5} of size 1200
   {3,5,2,5} of size 1200
   {5,5,2,5} of size 1200
   {6,5,2,5} of size 1200
   {6,5,2,5} of size 1200
   {10,5,2,5} of size 1200
   {10,5,2,5} of size 1200
   {4,5,2,5} of size 1600
   {5,5,2,5} of size 1600
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,10}*200, {10,2,5}*200
   3-fold covers : {5,2,15}*300, {15,2,5}*300
   4-fold covers : {5,2,20}*400, {20,2,5}*400, {10,2,10}*400
   5-fold covers : {5,2,25}*500, {25,2,5}*500, {5,10,5}*500
   6-fold covers : {5,2,30}*600, {10,2,15}*600, {15,2,10}*600, {30,2,5}*600
   7-fold covers : {5,2,35}*700, {35,2,5}*700
   8-fold covers : {5,2,40}*800, {40,2,5}*800, {10,2,20}*800, {20,2,10}*800, {10,4,10}*800
   9-fold covers : {5,2,45}*900, {45,2,5}*900, {15,2,15}*900
   10-fold covers : {5,2,50}*1000, {10,2,25}*1000, {25,2,10}*1000, {50,2,5}*1000, {5,10,10}*1000a, {10,10,5}*1000a, {5,10,10}*1000b, {10,10,5}*1000b
   11-fold covers : {5,2,55}*1100, {55,2,5}*1100
   12-fold covers : {15,2,20}*1200, {20,2,15}*1200, {5,2,60}*1200, {60,2,5}*1200, {10,6,10}*1200, {10,2,30}*1200, {30,2,10}*1200
   13-fold covers : {5,2,65}*1300, {65,2,5}*1300
   14-fold covers : {5,2,70}*1400, {10,2,35}*1400, {35,2,10}*1400, {70,2,5}*1400
   15-fold covers : {5,2,75}*1500, {75,2,5}*1500, {15,2,25}*1500, {25,2,15}*1500, {5,10,15}*1500, {15,10,5}*1500
   16-fold covers : {5,2,80}*1600, {80,2,5}*1600, {20,2,20}*1600, {10,4,20}*1600, {20,4,10}*1600, {10,2,40}*1600, {40,2,10}*1600, {10,8,10}*1600
   17-fold covers : {5,2,85}*1700, {85,2,5}*1700
   18-fold covers : {5,2,90}*1800, {10,2,45}*1800, {45,2,10}*1800, {90,2,5}*1800, {10,6,15}*1800, {15,6,10}*1800, {15,2,30}*1800, {30,2,15}*1800
   19-fold covers : {5,2,95}*1900, {95,2,5}*1900
   20-fold covers : {20,2,25}*2000, {25,2,20}*2000, {5,2,100}*2000, {100,2,5}*2000, {5,10,20}*2000a, {20,10,5}*2000a, {10,2,50}*2000, {50,2,10}*2000, {10,10,10}*2000a, {5,10,20}*2000b, {20,10,5}*2000b, {10,10,10}*2000b, {10,10,10}*2000c, {10,10,10}*2000g
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10);;
s3 := (6,7)(8,9);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(2,3)(4,5);
s1 := Sym(10)!(1,2)(3,4);
s2 := Sym(10)!( 7, 8)( 9,10);
s3 := Sym(10)!(6,7)(8,9);
poly := sub<Sym(10)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope