Polytope of Type {30,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,2,2}*240
if this polytope has a name.
Group : SmallGroup(240,207)
Rank : 4
Schlafli Type : {30,2,2}
Number of vertices, edges, etc : 30, 30, 2, 2
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {30,2,2,2} of size 480
   {30,2,2,3} of size 720
   {30,2,2,4} of size 960
   {30,2,2,5} of size 1200
   {30,2,2,6} of size 1440
   {30,2,2,7} of size 1680
   {30,2,2,8} of size 1920
Vertex Figure Of :
   {2,30,2,2} of size 480
   {4,30,2,2} of size 960
   {4,30,2,2} of size 960
   {4,30,2,2} of size 960
   {6,30,2,2} of size 1440
   {6,30,2,2} of size 1440
   {6,30,2,2} of size 1440
   {8,30,2,2} of size 1920
   {6,30,2,2} of size 1920
   {4,30,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,2,2}*120
   3-fold quotients : {10,2,2}*80
   5-fold quotients : {6,2,2}*48
   6-fold quotients : {5,2,2}*40
   10-fold quotients : {3,2,2}*24
   15-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,2,2}*480, {30,2,4}*480, {30,4,2}*480a
   3-fold covers : {90,2,2}*720, {30,2,6}*720, {30,6,2}*720b, {30,6,2}*720c
   4-fold covers : {60,4,2}*960a, {60,2,4}*960, {30,4,4}*960, {120,2,2}*960, {30,2,8}*960, {30,8,2}*960, {30,4,2}*960
   5-fold covers : {150,2,2}*1200, {30,2,10}*1200, {30,10,2}*1200b, {30,10,2}*1200c
   6-fold covers : {180,2,2}*1440, {90,2,4}*1440, {90,4,2}*1440a, {30,2,12}*1440, {30,12,2}*1440b, {60,2,6}*1440, {60,6,2}*1440b, {60,6,2}*1440c, {30,4,6}*1440, {30,6,4}*1440b, {30,6,4}*1440c, {30,12,2}*1440c
   7-fold covers : {30,2,14}*1680, {30,14,2}*1680, {210,2,2}*1680
   8-fold covers : {60,4,4}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {60,8,2}*1920a, {120,4,2}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {60,8,2}*1920b, {120,4,2}*1920b, {30,4,4}*1920a, {60,4,2}*1920a, {60,2,8}*1920, {120,2,4}*1920, {30,2,16}*1920, {30,16,2}*1920, {240,2,2}*1920, {60,4,2}*1920b, {30,4,4}*1920d, {30,4,2}*1920b, {60,4,2}*1920c, {30,8,2}*1920b, {30,8,2}*1920c
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,16)(17,20)(18,19)(21,22)
(23,26)(24,25)(27,30)(28,29);;
s1 := ( 1,17)( 2,11)( 3, 9)( 4,19)( 5, 7)( 6,27)( 8,13)(10,23)(12,21)(14,29)
(15,18)(16,28)(20,25)(22,24)(26,30);;
s2 := (31,32);;
s3 := (33,34);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(34)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,16)(17,20)(18,19)
(21,22)(23,26)(24,25)(27,30)(28,29);
s1 := Sym(34)!( 1,17)( 2,11)( 3, 9)( 4,19)( 5, 7)( 6,27)( 8,13)(10,23)(12,21)
(14,29)(15,18)(16,28)(20,25)(22,24)(26,30);
s2 := Sym(34)!(31,32);
s3 := Sym(34)!(33,34);
poly := sub<Sym(34)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope