Polytope of Type {2,2,30}

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

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

to this polytope