Polytope of Type {10,2,6}

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

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

to this polytope