Polytope of Type {2,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,5}*240a
if this polytope has a name.
Group : SmallGroup(240,190)
Rank : 4
Schlafli Type : {2,10,5}
Number of vertices, edges, etc : 2, 12, 30, 6
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,5,2} of size 480
Vertex Figure Of :
   {2,2,10,5} of size 480
   {3,2,10,5} of size 720
   {4,2,10,5} of size 960
   {5,2,10,5} of size 1200
   {6,2,10,5} of size 1440
   {7,2,10,5} of size 1680
   {8,2,10,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,5,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,10,5}*480, {2,10,5}*480, {2,10,10}*480b, {2,10,10}*480c
   3-fold covers : {6,10,5}*720
   4-fold covers : {8,10,5}*960, {4,10,5}*960, {4,10,10}*960a, {4,10,10}*960b, {2,20,10}*960a, {2,20,10}*960b, {2,20,5}*960, {2,10,10}*960
   5-fold covers : {10,10,5}*1200
   6-fold covers : {12,10,5}*1440, {6,10,5}*1440, {6,10,10}*1440a, {6,10,10}*1440b, {2,10,15}*1440, {2,30,10}*1440a
   7-fold covers : {14,10,5}*1680
   8-fold covers : {16,10,5}*1920, {4,20,10}*1920a, {4,20,10}*1920b, {8,10,5}*1920, {8,10,10}*1920a, {8,10,10}*1920b, {2,40,10}*1920a, {2,40,10}*1920b, {4,10,10}*1920, {2,10,20}*1920a, {2,20,10}*1920a, {4,20,5}*1920, {2,10,20}*1920b, {2,20,10}*1920b, {2,10,10}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,11)( 6,14)( 7, 9)( 8,10);;
s2 := ( 3, 4)( 5,13)( 6, 7)( 8,14)( 9,11)(10,12);;
s3 := ( 3,13)( 4,11)( 5,12)( 6, 7)( 8,10)( 9,14);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s3*s2*s1*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope