Polytope of Type {2,6,10}

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

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

to this polytope