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Polytope of Type {60,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,2,4}*960
if this polytope has a name.
Group : SmallGroup(960,10503)
Rank : 4
Schlafli Type : {60,2,4}
Number of vertices, edges, etc : 60, 60, 4, 4
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {60,2,4,2} of size 1920
Vertex Figure Of :
   {2,60,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,2,2}*480, {30,2,4}*480
   3-fold quotients : {20,2,4}*320
   4-fold quotients : {15,2,4}*240, {30,2,2}*240
   5-fold quotients : {12,2,4}*192
   6-fold quotients : {20,2,2}*160, {10,2,4}*160
   8-fold quotients : {15,2,2}*120
   10-fold quotients : {12,2,2}*96, {6,2,4}*96
   12-fold quotients : {5,2,4}*80, {10,2,2}*80
   15-fold quotients : {4,2,4}*64
   20-fold quotients : {3,2,4}*48, {6,2,2}*48
   24-fold quotients : {5,2,2}*40
   30-fold quotients : {2,2,4}*32, {4,2,2}*32
   40-fold quotients : {3,2,2}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,4,4}*1920, {60,2,8}*1920, {120,2,4}*1920
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 9,14)(10,13)(11,16)(12,15)(17,20)(18,19)(21,22)
(23,24)(25,26)(27,36)(28,35)(29,34)(30,33)(31,38)(32,37)(39,42)(40,41)(43,46)
(44,45)(47,48)(49,56)(50,55)(51,54)(52,53)(57,60)(58,59);;
s1 := ( 1,27)( 2,17)( 3,43)( 4,11)( 5,29)( 6, 9)( 7,49)( 8,33)(10,19)(12,39)
(13,25)(14,45)(15,23)(16,57)(18,31)(20,51)(21,28)(22,50)(24,35)(26,53)(30,41)
(32,40)(34,47)(36,59)(37,44)(38,58)(42,52)(46,55)(48,54)(56,60);;
s2 := (62,63);;
s3 := (61,62)(63,64);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, 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*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(64)!( 2, 3)( 4, 5)( 6, 7)( 9,14)(10,13)(11,16)(12,15)(17,20)(18,19)
(21,22)(23,24)(25,26)(27,36)(28,35)(29,34)(30,33)(31,38)(32,37)(39,42)(40,41)
(43,46)(44,45)(47,48)(49,56)(50,55)(51,54)(52,53)(57,60)(58,59);
s1 := Sym(64)!( 1,27)( 2,17)( 3,43)( 4,11)( 5,29)( 6, 9)( 7,49)( 8,33)(10,19)
(12,39)(13,25)(14,45)(15,23)(16,57)(18,31)(20,51)(21,28)(22,50)(24,35)(26,53)
(30,41)(32,40)(34,47)(36,59)(37,44)(38,58)(42,52)(46,55)(48,54)(56,60);
s2 := Sym(64)!(62,63);
s3 := Sym(64)!(61,62)(63,64);
poly := sub<Sym(64)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
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*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 >; 
 

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