Polytope of Type {2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30}*120
if this polytope has a name.
Group : SmallGroup(120,46)
Rank : 3
Schlafli Type : {2,30}
Number of vertices, edges, etc : 2, 30, 30
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,30,2} of size 240
   {2,30,4} of size 480
   {2,30,4} of size 480
   {2,30,4} of size 480
   {2,30,6} of size 720
   {2,30,6} of size 720
   {2,30,6} of size 720
   {2,30,8} of size 960
   {2,30,6} of size 960
   {2,30,4} of size 960
   {2,30,6} of size 1080
   {2,30,10} of size 1200
   {2,30,10} of size 1200
   {2,30,10} of size 1200
   {2,30,12} of size 1440
   {2,30,12} of size 1440
   {2,30,12} of size 1440
   {2,30,3} of size 1440
   {2,30,6} of size 1440
   {2,30,6} of size 1440
   {2,30,10} of size 1440
   {2,30,10} of size 1440
   {2,30,4} of size 1440
   {2,30,12} of size 1440
   {2,30,14} of size 1680
   {2,30,3} of size 1800
   {2,30,6} of size 1800
   {2,30,15} of size 1800
   {2,30,16} of size 1920
   {2,30,4} of size 1920
   {2,30,8} of size 1920
   {2,30,12} of size 1920
   {2,30,6} of size 1920
   {2,30,12} of size 1920
   {2,30,4} of size 1920
   {2,30,8} of size 1920
   {2,30,8} of size 1920
   {2,30,4} of size 1920
   {2,30,4} of size 1920
Vertex Figure Of :
   {2,2,30} of size 240
   {3,2,30} of size 360
   {4,2,30} of size 480
   {5,2,30} of size 600
   {6,2,30} of size 720
   {7,2,30} of size 840
   {8,2,30} of size 960
   {9,2,30} of size 1080
   {10,2,30} of size 1200
   {11,2,30} of size 1320
   {12,2,30} of size 1440
   {13,2,30} of size 1560
   {14,2,30} of size 1680
   {15,2,30} of size 1800
   {16,2,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,15}*60
   3-fold quotients : {2,10}*40
   5-fold quotients : {2,6}*24
   6-fold quotients : {2,5}*20
   10-fold quotients : {2,3}*12
   15-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,60}*240, {4,30}*240a
   3-fold covers : {2,90}*360, {6,30}*360b, {6,30}*360c
   4-fold covers : {4,60}*480a, {2,120}*480, {8,30}*480, {4,30}*480
   5-fold covers : {2,150}*600, {10,30}*600b, {10,30}*600c
   6-fold covers : {2,180}*720, {4,90}*720a, {12,30}*720b, {6,60}*720b, {6,60}*720c, {12,30}*720c
   7-fold covers : {14,30}*840, {2,210}*840
   8-fold covers : {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b, {2,240}*960, {16,30}*960, {4,60}*960b, {4,30}*960b, {4,60}*960c, {8,30}*960b, {8,30}*960c
   9-fold covers : {2,270}*1080, {6,90}*1080a, {6,90}*1080b, {18,30}*1080b, {6,30}*1080b, {6,30}*1080c, {6,30}*1080d
   10-fold covers : {2,300}*1200, {4,150}*1200a, {20,30}*1200b, {10,60}*1200b, {10,60}*1200c, {20,30}*1200c
   11-fold covers : {22,30}*1320, {2,330}*1320
   12-fold covers : {4,180}*1440a, {2,360}*1440, {8,90}*1440, {24,30}*1440b, {6,120}*1440b, {6,120}*1440c, {12,60}*1440b, {12,60}*1440c, {24,30}*1440c, {4,90}*1440, {12,30}*1440a, {12,30}*1440b, {6,30}*1440h, {6,60}*1440d
   13-fold covers : {26,30}*1560, {2,390}*1560
   14-fold covers : {14,60}*1680, {28,30}*1680a, {2,420}*1680, {4,210}*1680a
   15-fold covers : {2,450}*1800, {6,150}*1800b, {6,150}*1800c, {10,90}*1800b, {10,90}*1800c, {30,30}*1800c, {30,30}*1800d, {30,30}*1800g, {30,30}*1800h
   16-fold covers : {8,60}*1920a, {4,120}*1920a, {8,120}*1920a, {8,120}*1920b, {8,120}*1920c, {8,120}*1920d, {16,60}*1920a, {4,240}*1920a, {16,60}*1920b, {4,240}*1920b, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {32,30}*1920, {2,480}*1920, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,30}*1920a, {8,30}*1920d, {8,30}*1920e, {8,30}*1920f, {8,60}*1920g, {8,60}*1920h, {4,120}*1920c, {4,120}*1920d, {8,30}*1920g, {4,60}*1920e, {4,120}*1920e, {4,30}*1920b, {4,120}*1920f, {4,30}*1920d
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(32)!(1,2);
s1 := Sym(32)!( 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(32)!( 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);
poly := sub<Sym(32)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

to this polytope