Polytope of Type {4,2,60,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,60,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,208115)
Rank : 5
Schlafli Type : {4,2,60,2}
Number of vertices, edges, etc : 4, 4, 60, 60, 2
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,60,2}*960, {4,2,30,2}*960
   3-fold quotients : {4,2,20,2}*640
   4-fold quotients : {4,2,15,2}*480, {2,2,30,2}*480
   5-fold quotients : {4,2,12,2}*384
   6-fold quotients : {2,2,20,2}*320, {4,2,10,2}*320
   8-fold quotients : {2,2,15,2}*240
   10-fold quotients : {2,2,12,2}*192, {4,2,6,2}*192
   12-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   15-fold quotients : {4,2,4,2}*128
   20-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,3,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(13,18)(14,17)(15,20)(16,19)(21,24)(22,23)(25,26)
(27,28)(29,30)(31,40)(32,39)(33,38)(34,37)(35,42)(36,41)(43,46)(44,45)(47,50)
(48,49)(51,52)(53,60)(54,59)(55,58)(56,57)(61,64)(62,63);;
s3 := ( 5,31)( 6,21)( 7,47)( 8,15)( 9,33)(10,13)(11,53)(12,37)(14,23)(16,43)
(17,29)(18,49)(19,27)(20,61)(22,35)(24,55)(25,32)(26,54)(28,39)(30,57)(34,45)
(36,44)(38,51)(40,63)(41,48)(42,62)(46,56)(50,59)(52,58)(60,64);;
s4 := (65,66);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!(2,3);
s1 := Sym(66)!(1,2)(3,4);
s2 := Sym(66)!( 6, 7)( 8, 9)(10,11)(13,18)(14,17)(15,20)(16,19)(21,24)(22,23)
(25,26)(27,28)(29,30)(31,40)(32,39)(33,38)(34,37)(35,42)(36,41)(43,46)(44,45)
(47,50)(48,49)(51,52)(53,60)(54,59)(55,58)(56,57)(61,64)(62,63);
s3 := Sym(66)!( 5,31)( 6,21)( 7,47)( 8,15)( 9,33)(10,13)(11,53)(12,37)(14,23)
(16,43)(17,29)(18,49)(19,27)(20,61)(22,35)(24,55)(25,32)(26,54)(28,39)(30,57)
(34,45)(36,44)(38,51)(40,63)(41,48)(42,62)(46,56)(50,59)(52,58)(60,64);
s4 := Sym(66)!(65,66);
poly := sub<Sym(66)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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