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Polytope of Type {4,30,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,2}*480a
if this polytope has a name.
Group : SmallGroup(480,1169)
Rank : 4
Schlafli Type : {4,30,2}
Number of vertices, edges, etc : 4, 60, 30, 2
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,30,2,2} of size 960
   {4,30,2,3} of size 1440
   {4,30,2,4} of size 1920
Vertex Figure Of :
   {2,4,30,2} of size 960
   {4,4,30,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,30,2}*240
   3-fold quotients : {4,10,2}*160
   4-fold quotients : {2,15,2}*120
   5-fold quotients : {4,6,2}*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 : {4,2,2}*32
   20-fold quotients : {2,3,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,60,2}*960a, {4,30,4}*960a, {8,30,2}*960
   3-fold covers : {4,90,2}*1440a, {12,30,2}*1440b, {4,30,6}*1440b, {4,30,6}*1440c, {12,30,2}*1440c
   4-fold covers : {4,60,4}*1920a, {8,60,2}*1920a, {4,120,2}*1920a, {8,60,2}*1920b, {4,120,2}*1920b, {4,60,2}*1920a, {4,30,8}*1920a, {8,30,4}*1920a, {16,30,2}*1920, {4,30,4}*1920a, {4,30,2}*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);;
s3 := (61,62);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
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(62)!(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(62)!( 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(62)!( 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);
s3 := Sym(62)!(61,62);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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 >; 
 

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