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Polytope of Type {30,4}

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