Polytope of Type {2,30,2}

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

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

Permutation Representation (Magma) :

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

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