Polytope of Type {2,10,6}

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

s0 := (1,2);;
s1 := ( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30)(31,32);;
s2 := ( 3, 7)( 4,11)( 5,15)( 6,13)( 8,17)( 9,21)(10,19)(12,23)(14,27)(16,25)
(20,31)(22,29)(26,28)(30,32);;
s3 := ( 3, 9)( 4, 5)( 6,10)( 7,19)( 8,20)(11,13)(12,14)(15,21)(16,22)(17,29)
(18,30)(23,25)(24,26)(27,31)(28,32);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!(1,2);
s1 := Sym(32)!( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)
(27,28)(29,30)(31,32);
s2 := Sym(32)!( 3, 7)( 4,11)( 5,15)( 6,13)( 8,17)( 9,21)(10,19)(12,23)(14,27)
(16,25)(20,31)(22,29)(26,28)(30,32);
s3 := Sym(32)!( 3, 9)( 4, 5)( 6,10)( 7,19)( 8,20)(11,13)(12,14)(15,21)(16,22)
(17,29)(18,30)(23,25)(24,26)(27,31)(28,32);
poly := sub<Sym(32)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope