Polytope of Type {3,2,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,10}*240
if this polytope has a name.
Group : SmallGroup(240,202)
Rank : 5
Schlafli Type : {3,2,2,10}
Number of vertices, edges, etc : 3, 3, 2, 10, 10
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,10,2} of size 480
   {3,2,2,10,4} of size 960
   {3,2,2,10,5} of size 1200
   {3,2,2,10,3} of size 1440
   {3,2,2,10,3} of size 1440
   {3,2,2,10,5} of size 1440
   {3,2,2,10,5} of size 1440
   {3,2,2,10,6} of size 1440
   {3,2,2,10,8} of size 1920
Vertex Figure Of :
   {2,3,2,2,10} of size 480
   {3,3,2,2,10} of size 960
   {4,3,2,2,10} of size 960
   {6,3,2,2,10} of size 1440
   {4,3,2,2,10} of size 1920
   {6,3,2,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,5}*120
   5-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,2,20}*480, {3,2,4,10}*480, {6,2,2,10}*480
   3-fold covers : {9,2,2,10}*720, {3,2,6,10}*720, {3,6,2,10}*720, {3,2,2,30}*720
   4-fold covers : {3,2,4,20}*960, {3,2,2,40}*960, {3,2,8,10}*960, {12,2,2,10}*960, {6,2,2,20}*960, {6,2,4,10}*960, {6,4,2,10}*960a, {3,4,2,10}*960
   5-fold covers : {3,2,2,50}*1200, {3,2,10,10}*1200a, {3,2,10,10}*1200b, {15,2,2,10}*1200
   6-fold covers : {9,2,2,20}*1440, {9,2,4,10}*1440, {18,2,2,10}*1440, {3,2,12,10}*1440, {3,2,6,20}*1440a, {3,6,2,20}*1440, {3,6,4,10}*1440, {3,2,2,60}*1440, {3,2,4,30}*1440a, {6,2,6,10}*1440, {6,6,2,10}*1440a, {6,6,2,10}*1440c, {6,2,2,30}*1440
   7-fold covers : {3,2,14,10}*1680, {21,2,2,10}*1680, {3,2,2,70}*1680
   8-fold covers : {3,2,8,20}*1920a, {3,2,4,40}*1920a, {3,2,8,20}*1920b, {3,2,4,40}*1920b, {3,2,4,20}*1920, {3,2,16,10}*1920, {3,2,2,80}*1920, {6,4,4,10}*1920, {12,4,2,10}*1920a, {6,2,4,20}*1920, {12,2,4,10}*1920, {6,4,2,20}*1920a, {12,2,2,20}*1920, {6,2,8,10}*1920, {6,8,2,10}*1920, {24,2,2,10}*1920, {6,2,2,40}*1920, {3,4,2,20}*1920, {3,4,4,10}*1920b, {3,8,2,10}*1920, {6,4,2,10}*1920
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 8, 9)(10,11)(12,13)(14,15);;
s4 := ( 6,10)( 7, 8)( 9,14)(11,12)(13,15);;
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*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, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!(2,3);
s1 := Sym(15)!(1,2);
s2 := Sym(15)!(4,5);
s3 := Sym(15)!( 8, 9)(10,11)(12,13)(14,15);
s4 := Sym(15)!( 6,10)( 7, 8)( 9,14)(11,12)(13,15);
poly := sub<Sym(15)|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*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, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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