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Polytope of Type {4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30}*240a
Also Known As : {4,30|2}. if this polytope has another name.
Group : SmallGroup(240,179)
Rank : 3
Schlafli Type : {4,30}
Number of vertices, edges, etc : 4, 60, 30
Order of s0s1s2 : 60
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,30,2} of size 480
   {4,30,4} of size 960
   {4,30,4} of size 960
   {4,30,6} of size 1440
   {4,30,6} of size 1440
   {4,30,6} of size 1440
   {4,30,8} of size 1920
   {4,30,6} of size 1920
   {4,30,4} of size 1920
Vertex Figure Of :
   {2,4,30} of size 480
   {4,4,30} of size 960
   {6,4,30} of size 1440
   {3,4,30} of size 1440
   {8,4,30} of size 1920
   {8,4,30} of size 1920
   {4,4,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,30}*120
   3-fold quotients : {4,10}*80
   4-fold quotients : {2,15}*60
   5-fold quotients : {4,6}*48a
   6-fold quotients : {2,10}*40
   10-fold quotients : {2,6}*24
   12-fold quotients : {2,5}*20
   15-fold quotients : {4,2}*16
   20-fold quotients : {2,3}*12
   30-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,60}*480a, {8,30}*480
   3-fold covers : {4,90}*720a, {12,30}*720b, {12,30}*720c
   4-fold covers : {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b, {16,30}*960, {4,30}*960b
   5-fold covers : {4,150}*1200a, {20,30}*1200b, {20,30}*1200c
   6-fold covers : {4,180}*1440a, {8,90}*1440, {24,30}*1440b, {12,60}*1440b, {12,60}*1440c, {24,30}*1440c
   7-fold covers : {28,30}*1680a, {4,210}*1680a
   8-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, {4,60}*1920d, {8,30}*1920f, {8,30}*1920g, {4,60}*1920e, {4,30}*1920b
Permutation Representation (GAP) :
s0 := (31,46)(32,47)(33,48)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)
(41,56)(42,57)(43,58)(44,59)(45,60);;
s1 := ( 1,31)( 2,35)( 3,34)( 4,33)( 5,32)( 6,41)( 7,45)( 8,44)( 9,43)(10,42)
(11,36)(12,40)(13,39)(14,38)(15,37)(16,46)(17,50)(18,49)(19,48)(20,47)(21,56)
(22,60)(23,59)(24,58)(25,57)(26,51)(27,55)(28,54)(29,53)(30,52);;
s2 := ( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,22)(17,21)(18,25)
(19,24)(20,23)(26,27)(28,30)(31,37)(32,36)(33,40)(34,39)(35,38)(41,42)(43,45)
(46,52)(47,51)(48,55)(49,54)(50,53)(56,57)(58,60);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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(60)!(31,46)(32,47)(33,48)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)
(40,55)(41,56)(42,57)(43,58)(44,59)(45,60);
s1 := Sym(60)!( 1,31)( 2,35)( 3,34)( 4,33)( 5,32)( 6,41)( 7,45)( 8,44)( 9,43)
(10,42)(11,36)(12,40)(13,39)(14,38)(15,37)(16,46)(17,50)(18,49)(19,48)(20,47)
(21,56)(22,60)(23,59)(24,58)(25,57)(26,51)(27,55)(28,54)(29,53)(30,52);
s2 := Sym(60)!( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,22)(17,21)
(18,25)(19,24)(20,23)(26,27)(28,30)(31,37)(32,36)(33,40)(34,39)(35,38)(41,42)
(43,45)(46,52)(47,51)(48,55)(49,54)(50,53)(56,57)(58,60);
poly := sub<Sym(60)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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 >; 
 
References : None.
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