Polytope of Type {6,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,10}*240
if this polytope has a name.
Group : SmallGroup(240,202)
Rank : 4
Schlafli Type : {6,2,10}
Number of vertices, edges, etc : 6, 6, 10, 10
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,10,2} of size 480
   {6,2,10,4} of size 960
   {6,2,10,5} of size 1200
   {6,2,10,3} of size 1440
   {6,2,10,3} of size 1440
   {6,2,10,5} of size 1440
   {6,2,10,5} of size 1440
   {6,2,10,6} of size 1440
   {6,2,10,8} of size 1920
Vertex Figure Of :
   {2,6,2,10} of size 480
   {3,6,2,10} of size 720
   {4,6,2,10} of size 960
   {3,6,2,10} of size 960
   {4,6,2,10} of size 960
   {4,6,2,10} of size 960
   {4,6,2,10} of size 1440
   {6,6,2,10} of size 1440
   {6,6,2,10} of size 1440
   {6,6,2,10} of size 1440
   {8,6,2,10} of size 1920
   {4,6,2,10} of size 1920
   {6,6,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,10}*120, {6,2,5}*120
   3-fold quotients : {2,2,10}*80
   4-fold quotients : {3,2,5}*60
   5-fold quotients : {6,2,2}*48
   6-fold quotients : {2,2,5}*40
   10-fold quotients : {3,2,2}*24
   15-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,10}*480, {6,2,20}*480, {6,4,10}*480
   3-fold covers : {18,2,10}*720, {6,6,10}*720a, {6,6,10}*720c, {6,2,30}*720
   4-fold covers : {12,2,20}*960, {12,4,10}*960, {6,4,20}*960, {24,2,10}*960, {6,2,40}*960, {6,8,10}*960, {6,4,10}*960
   5-fold covers : {6,2,50}*1200, {6,10,10}*1200a, {6,10,10}*1200b, {30,2,10}*1200
   6-fold covers : {36,2,10}*1440, {18,2,20}*1440, {18,4,10}*1440, {6,12,10}*1440a, {12,6,10}*1440a, {12,6,10}*1440b, {6,6,20}*1440a, {6,6,20}*1440c, {6,12,10}*1440c, {12,2,30}*1440, {6,2,60}*1440, {6,4,30}*1440
   7-fold covers : {6,14,10}*1680, {42,2,10}*1680, {6,2,70}*1680
   8-fold covers : {12,4,20}*1920, {12,8,10}*1920a, {6,8,20}*1920a, {24,4,10}*1920a, {6,4,40}*1920a, {12,8,10}*1920b, {6,8,20}*1920b, {24,4,10}*1920b, {6,4,40}*1920b, {12,4,10}*1920a, {6,4,20}*1920a, {12,2,40}*1920, {24,2,20}*1920, {6,16,10}*1920, {48,2,10}*1920, {6,2,80}*1920, {12,4,10}*1920b, {6,4,20}*1920b, {6,4,10}*1920, {12,4,10}*1920c, {6,8,10}*1920a, {6,8,10}*1920b
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 9,10)(11,12)(13,14)(15,16);;
s3 := ( 7,11)( 8, 9)(10,15)(12,13)(14,16);;
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*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(16)!(3,4)(5,6);
s1 := Sym(16)!(1,5)(2,3)(4,6);
s2 := Sym(16)!( 9,10)(11,12)(13,14)(15,16);
s3 := Sym(16)!( 7,11)( 8, 9)(10,15)(12,13)(14,16);
poly := sub<Sym(16)|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*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope