Polytope of Type {3,2,2,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,2,5}*240
if this polytope has a name.
Group : SmallGroup(240,202)
Rank : 6
Schlafli Type : {3,2,2,2,5}
Number of vertices, edges, etc : 3, 3, 2, 2, 5, 5
Order of s₀s₁s₂s₃s₄s₅ : 30
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,2,5,2} of size 480
   {3,2,2,2,5,3} of size 1440
   {3,2,2,2,5,5} of size 1440
Vertex Figure Of :
   {2,3,2,2,2,5} of size 480
   {3,3,2,2,2,5} of size 960
   {4,3,2,2,2,5} of size 960
   {6,3,2,2,2,5} of size 1440
   {4,3,2,2,2,5} of size 1920
   {6,3,2,2,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,2,5}*480, {3,2,2,2,10}*480, {6,2,2,2,5}*480
   3-fold covers : {9,2,2,2,5}*720, {3,2,6,2,5}*720, {3,6,2,2,5}*720, {3,2,2,2,15}*720
   4-fold covers : {3,2,8,2,5}*960, {12,2,2,2,5}*960, {3,2,2,2,20}*960, {3,2,2,4,10}*960, {3,2,4,2,10}*960, {6,2,4,2,5}*960, {6,4,2,2,5}*960a, {3,4,2,2,5}*960, {6,2,2,2,10}*960
   5-fold covers : {3,2,2,2,25}*1200, {3,2,2,10,5}*1200, {3,2,10,2,5}*1200, {15,2,2,2,5}*1200
   6-fold covers : {9,2,4,2,5}*1440, {9,2,2,2,10}*1440, {18,2,2,2,5}*1440, {3,2,12,2,5}*1440, {3,6,4,2,5}*1440, {3,2,4,2,15}*1440, {3,2,2,6,10}*1440, {3,2,6,2,10}*1440, {3,6,2,2,10}*1440, {6,2,6,2,5}*1440, {6,6,2,2,5}*1440a, {6,6,2,2,5}*1440c, {3,2,2,2,30}*1440, {6,2,2,2,15}*1440
   7-fold covers : {3,2,14,2,5}*1680, {21,2,2,2,5}*1680, {3,2,2,2,35}*1680
   8-fold covers : {3,2,16,2,5}*1920, {3,2,4,4,10}*1920, {6,4,4,2,5}*1920, {12,4,2,2,5}*1920a, {3,2,2,4,20}*1920, {12,2,4,2,5}*1920, {3,2,4,2,20}*1920, {3,2,2,8,10}*1920, {3,2,8,2,10}*1920, {6,2,8,2,5}*1920, {6,8,2,2,5}*1920, {24,2,2,2,5}*1920, {3,2,2,2,40}*1920, {6,2,2,4,10}*1920, {6,2,4,2,10}*1920, {6,4,2,2,10}*1920a, {12,2,2,2,10}*1920, {6,2,2,2,20}*1920, {3,4,4,2,5}*1920b, {3,8,2,2,5}*1920, {3,4,2,2,10}*1920, {6,4,2,2,5}*1920
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := (6,7);;
s4 := ( 9,10)(11,12);;
s5 := ( 8, 9)(10,11);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!(2,3);
s1 := Sym(12)!(1,2);
s2 := Sym(12)!(4,5);
s3 := Sym(12)!(6,7);
s4 := Sym(12)!( 9,10)(11,12);
s5 := Sym(12)!( 8, 9)(10,11);
poly := sub<Sym(12)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope