Polytope of Type {10,6,2}

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

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

to this polytope