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Polytope of Type {60,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,2}*240
if this polytope has a name.
Group : SmallGroup(240,177)
Rank : 3
Schlafli Type : {60,2}
Number of vertices, edges, etc : 60, 60, 2
Order of s0s1s2 : 60
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {60,2,2} of size 480
   {60,2,3} of size 720
   {60,2,4} of size 960
   {60,2,5} of size 1200
   {60,2,6} of size 1440
   {60,2,7} of size 1680
   {60,2,8} of size 1920
Vertex Figure Of :
   {2,60,2} of size 480
   {4,60,2} of size 960
   {4,60,2} of size 960
   {4,60,2} of size 960
   {6,60,2} of size 1440
   {6,60,2} of size 1440
   {6,60,2} of size 1440
   {6,60,2} of size 1440
   {8,60,2} of size 1920
   {8,60,2} of size 1920
   {4,60,2} of size 1920
   {6,60,2} of size 1920
   {6,60,2} of size 1920
   {4,60,2} of size 1920
   {4,60,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,2}*120
   3-fold quotients : {20,2}*80
   4-fold quotients : {15,2}*60
   5-fold quotients : {12,2}*48
   6-fold quotients : {10,2}*40
   10-fold quotients : {6,2}*24
   12-fold quotients : {5,2}*20
   15-fold quotients : {4,2}*16
   20-fold quotients : {3,2}*12
   30-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,4}*480a, {120,2}*480
   3-fold covers : {180,2}*720, {60,6}*720b, {60,6}*720c
   4-fold covers : {120,4}*960a, {60,4}*960a, {120,4}*960b, {60,8}*960a, {60,8}*960b, {240,2}*960, {60,4}*960b
   5-fold covers : {300,2}*1200, {60,10}*1200b, {60,10}*1200c
   6-fold covers : {180,4}*1440a, {360,2}*1440, {120,6}*1440b, {120,6}*1440c, {60,12}*1440b, {60,12}*1440c
   7-fold covers : {60,14}*1680, {420,2}*1680
   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, {480,2}*1920, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {120,4}*1920c, {120,4}*1920d
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 := (61,62);;
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, 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*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(62)!( 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(62)!( 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(62)!(61,62);
poly := sub<Sym(62)|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, 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*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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