Polytope of Type {30,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,2}*120
if this polytope has a name.
Group : SmallGroup(120,46)
Rank : 3
Schlafli Type : {30,2}
Number of vertices, edges, etc : 30, 30, 2
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {30,2,2} of size 240
   {30,2,3} of size 360
   {30,2,4} of size 480
   {30,2,5} of size 600
   {30,2,6} of size 720
   {30,2,7} of size 840
   {30,2,8} of size 960
   {30,2,9} of size 1080
   {30,2,10} of size 1200
   {30,2,11} of size 1320
   {30,2,12} of size 1440
   {30,2,13} of size 1560
   {30,2,14} of size 1680
   {30,2,15} of size 1800
   {30,2,16} of size 1920
Vertex Figure Of :
   {2,30,2} of size 240
   {4,30,2} of size 480
   {4,30,2} of size 480
   {4,30,2} of size 480
   {6,30,2} of size 720
   {6,30,2} of size 720
   {6,30,2} of size 720
   {8,30,2} of size 960
   {6,30,2} of size 960
   {4,30,2} of size 960
   {6,30,2} of size 1080
   {10,30,2} of size 1200
   {10,30,2} of size 1200
   {10,30,2} of size 1200
   {12,30,2} of size 1440
   {12,30,2} of size 1440
   {12,30,2} of size 1440
   {3,30,2} of size 1440
   {6,30,2} of size 1440
   {6,30,2} of size 1440
   {10,30,2} of size 1440
   {10,30,2} of size 1440
   {4,30,2} of size 1440
   {12,30,2} of size 1440
   {14,30,2} of size 1680
   {3,30,2} of size 1800
   {6,30,2} of size 1800
   {15,30,2} of size 1800
   {16,30,2} of size 1920
   {4,30,2} of size 1920
   {8,30,2} of size 1920
   {12,30,2} of size 1920
   {6,30,2} of size 1920
   {12,30,2} of size 1920
   {4,30,2} of size 1920
   {8,30,2} of size 1920
   {8,30,2} of size 1920
   {4,30,2} of size 1920
   {4,30,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,2}*60
   3-fold quotients : {10,2}*40
   5-fold quotients : {6,2}*24
   6-fold quotients : {5,2}*20
   10-fold quotients : {3,2}*12
   15-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,2}*240, {30,4}*240a
   3-fold covers : {90,2}*360, {30,6}*360b, {30,6}*360c
   4-fold covers : {60,4}*480a, {120,2}*480, {30,8}*480, {30,4}*480
   5-fold covers : {150,2}*600, {30,10}*600b, {30,10}*600c
   6-fold covers : {180,2}*720, {90,4}*720a, {30,12}*720b, {60,6}*720b, {60,6}*720c, {30,12}*720c
   7-fold covers : {30,14}*840, {210,2}*840
   8-fold covers : {120,4}*960a, {60,4}*960a, {120,4}*960b, {60,8}*960a, {60,8}*960b, {240,2}*960, {30,16}*960, {60,4}*960b, {30,4}*960b, {60,4}*960c, {30,8}*960b, {30,8}*960c
   9-fold covers : {270,2}*1080, {90,6}*1080a, {90,6}*1080b, {30,18}*1080b, {30,6}*1080b, {30,6}*1080c, {30,6}*1080d
   10-fold covers : {300,2}*1200, {150,4}*1200a, {30,20}*1200b, {60,10}*1200b, {60,10}*1200c, {30,20}*1200c
   11-fold covers : {30,22}*1320, {330,2}*1320
   12-fold covers : {180,4}*1440a, {360,2}*1440, {90,8}*1440, {30,24}*1440b, {120,6}*1440b, {120,6}*1440c, {60,12}*1440b, {60,12}*1440c, {30,24}*1440c, {90,4}*1440, {30,12}*1440a, {30,12}*1440b, {30,6}*1440h, {60,6}*1440d
   13-fold covers : {30,26}*1560, {390,2}*1560
   14-fold covers : {60,14}*1680, {30,28}*1680a, {420,2}*1680, {210,4}*1680a
   15-fold covers : {450,2}*1800, {150,6}*1800b, {150,6}*1800c, {90,10}*1800b, {90,10}*1800c, {30,30}*1800a, {30,30}*1800f, {30,30}*1800g, {30,30}*1800i
   16-fold covers : {60,8}*1920a, {120,4}*1920a, {120,8}*1920a, {120,8}*1920b, {120,8}*1920c, {120,8}*1920d, {60,16}*1920a, {240,4}*1920a, {60,16}*1920b, {240,4}*1920b, {60,4}*1920a, {120,4}*1920b, {60,8}*1920b, {30,32}*1920, {480,2}*1920, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {30,4}*1920a, {30,8}*1920d, {30,8}*1920e, {30,8}*1920f, {60,8}*1920g, {60,8}*1920h, {120,4}*1920c, {120,4}*1920d, {30,8}*1920g, {60,4}*1920e, {120,4}*1920e, {30,4}*1920b, {120,4}*1920f, {30,4}*1920d
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);;
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*s2*s0*s2, s1*s2*s1*s2, 
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(32)!( 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(32)!( 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(32)!(31,32);
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*s2*s0*s2, s1*s2*s1*s2, 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