Polytope of Type {10,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,5}*200
if this polytope has a name.
Group : SmallGroup(200,49)
Rank : 4
Schlafli Type : {10,2,5}
Number of vertices, edges, etc : 10, 10, 5, 5
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,2,5,2} of size 400
   {10,2,5,3} of size 1200
   {10,2,5,5} of size 1200
   {10,2,5,10} of size 2000
Vertex Figure Of :
   {2,10,2,5} of size 400
   {4,10,2,5} of size 800
   {5,10,2,5} of size 1000
   {3,10,2,5} of size 1200
   {3,10,2,5} of size 1200
   {5,10,2,5} of size 1200
   {5,10,2,5} of size 1200
   {6,10,2,5} of size 1200
   {8,10,2,5} of size 1600
   {4,10,2,5} of size 2000
   {10,10,2,5} of size 2000
   {10,10,2,5} of size 2000
   {10,10,2,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,5}*100
   5-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,2,5}*400, {10,2,10}*400
   3-fold covers : {10,2,15}*600, {30,2,5}*600
   4-fold covers : {40,2,5}*800, {10,2,20}*800, {20,2,10}*800, {10,4,10}*800
   5-fold covers : {10,2,25}*1000, {50,2,5}*1000, {10,10,5}*1000a, {10,10,5}*1000b
   6-fold covers : {20,2,15}*1200, {60,2,5}*1200, {10,6,10}*1200, {10,2,30}*1200, {30,2,10}*1200
   7-fold covers : {10,2,35}*1400, {70,2,5}*1400
   8-fold covers : {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
   9-fold covers : {10,2,45}*1800, {90,2,5}*1800, {10,6,15}*1800, {30,2,15}*1800
   10-fold covers : {20,2,25}*2000, {100,2,5}*2000, {20,10,5}*2000a, {10,2,50}*2000, {50,2,10}*2000, {10,10,10}*2000a, {20,10,5}*2000b, {10,10,10}*2000b, {10,10,10}*2000c, {10,10,10}*2000g
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (12,13)(14,15);;
s3 := (11,12)(13,14);;
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, 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(15)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(15)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(15)!(12,13)(14,15);
s3 := Sym(15)!(11,12)(13,14);
poly := sub<Sym(15)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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