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Polytope of Type {2,30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,4}*480a
if this polytope has a name.
Group : SmallGroup(480,1169)
Rank : 4
Schlafli Type : {2,30,4}
Number of vertices, edges, etc : 2, 30, 60, 4
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,30,4,2} of size 960
   {2,30,4,4} of size 1920
Vertex Figure Of :
   {2,2,30,4} of size 960
   {3,2,30,4} of size 1440
   {4,2,30,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,30,2}*240
   3-fold quotients : {2,10,4}*160
   4-fold quotients : {2,15,2}*120
   5-fold quotients : {2,6,4}*96a
   6-fold quotients : {2,10,2}*80
   10-fold quotients : {2,6,2}*48
   12-fold quotients : {2,5,2}*40
   15-fold quotients : {2,2,4}*32
   20-fold quotients : {2,3,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,60,4}*960a, {4,30,4}*960a, {2,30,8}*960
   3-fold covers : {2,90,4}*1440a, {2,30,12}*1440b, {6,30,4}*1440b, {6,30,4}*1440c, {2,30,12}*1440c
   4-fold covers : {4,60,4}*1920a, {2,60,8}*1920a, {2,120,4}*1920a, {2,60,8}*1920b, {2,120,4}*1920b, {2,60,4}*1920a, {4,30,8}*1920a, {8,30,4}*1920a, {2,30,16}*1920, {4,30,4}*1920b, {2,30,4}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)(23,28)
(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)
(49,52)(50,51)(53,58)(54,62)(55,61)(56,60)(57,59);;
s2 := ( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,24)(19,23)(20,27)
(21,26)(22,25)(28,29)(30,32)(33,54)(34,53)(35,57)(36,56)(37,55)(38,49)(39,48)
(40,52)(41,51)(42,50)(43,59)(44,58)(45,62)(46,61)(47,60);;
s3 := ( 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)(31,61)(32,62);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*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(62)!(1,2);
s1 := Sym(62)!( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)
(23,28)(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)
(42,44)(49,52)(50,51)(53,58)(54,62)(55,61)(56,60)(57,59);
s2 := Sym(62)!( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,24)(19,23)
(20,27)(21,26)(22,25)(28,29)(30,32)(33,54)(34,53)(35,57)(36,56)(37,55)(38,49)
(39,48)(40,52)(41,51)(42,50)(43,59)(44,58)(45,62)(46,61)(47,60);
s3 := Sym(62)!( 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)(31,61)(32,62);
poly := sub<Sym(62)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*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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