Polytope of Type {2,2,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,30}*480
if this polytope has a name.
Group : SmallGroup(480,1212)
Rank : 5
Schlafli Type : {2,2,2,30}
Number of vertices, edges, etc : 2, 2, 2, 30, 30
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,30,2} of size 960
   {2,2,2,30,4} of size 1920
   {2,2,2,30,4} of size 1920
   {2,2,2,30,4} of size 1920
Vertex Figure Of :
   {2,2,2,2,30} of size 960
   {3,2,2,2,30} of size 1440
   {4,2,2,2,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,15}*240
   3-fold quotients : {2,2,2,10}*160
   5-fold quotients : {2,2,2,6}*96
   6-fold quotients : {2,2,2,5}*80
   10-fold quotients : {2,2,2,3}*48
   15-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,2,60}*960, {2,2,4,30}*960a, {2,4,2,30}*960, {4,2,2,30}*960
   3-fold covers : {2,2,2,90}*1440, {2,2,6,30}*1440b, {2,2,6,30}*1440c, {2,6,2,30}*1440, {6,2,2,30}*1440
   4-fold covers : {2,4,4,30}*1920, {4,4,2,30}*1920, {2,2,4,60}*1920a, {4,2,4,30}*1920a, {2,4,2,60}*1920, {4,2,2,60}*1920, {2,2,8,30}*1920, {2,8,2,30}*1920, {8,2,2,30}*1920, {2,2,2,120}*1920, {2,2,4,30}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 9,10)(11,12)(13,14)(15,16)(17,20)(18,19)(21,22)(23,26)(24,25)(27,28)
(29,32)(30,31)(33,36)(34,35);;
s4 := ( 7,23)( 8,17)( 9,15)(10,25)(11,13)(12,33)(14,19)(16,29)(18,27)(20,35)
(21,24)(22,34)(26,31)(28,30)(32,36);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(36)!(1,2);
s1 := Sym(36)!(3,4);
s2 := Sym(36)!(5,6);
s3 := Sym(36)!( 9,10)(11,12)(13,14)(15,16)(17,20)(18,19)(21,22)(23,26)(24,25)
(27,28)(29,32)(30,31)(33,36)(34,35);
s4 := Sym(36)!( 7,23)( 8,17)( 9,15)(10,25)(11,13)(12,33)(14,19)(16,29)(18,27)
(20,35)(21,24)(22,34)(26,31)(28,30)(32,36);
poly := sub<Sym(36)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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