Polytope of Type {6,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,10}*480
Also Known As : {{6,4|2},{4,10|2}}. if this polytope has another name.
Group : SmallGroup(480,1097)
Rank : 4
Schlafli Type : {6,4,10}
Number of vertices, edges, etc : 6, 12, 20, 10
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,4,10,2} of size 960
   {6,4,10,4} of size 1920
Vertex Figure Of :
   {2,6,4,10} of size 960
   {3,6,4,10} of size 1440
   {4,6,4,10} of size 1920
   {3,6,4,10} of size 1920
   {4,6,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,10}*240
   3-fold quotients : {2,4,10}*160
   4-fold quotients : {3,2,10}*120, {6,2,5}*120
   5-fold quotients : {6,4,2}*96a
   6-fold quotients : {2,2,10}*80
   8-fold quotients : {3,2,5}*60
   10-fold quotients : {6,2,2}*48
   12-fold quotients : {2,2,5}*40
   15-fold quotients : {2,4,2}*32
   20-fold quotients : {3,2,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,10}*960, {6,4,20}*960, {6,8,10}*960
   3-fold covers : {18,4,10}*1440, {6,12,10}*1440a, {6,12,10}*1440c, {6,4,30}*1440
   4-fold covers : {12,4,20}*1920, {12,8,10}*1920a, {6,8,20}*1920a, {24,4,10}*1920a, {6,4,40}*1920a, {12,8,10}*1920b, {6,8,20}*1920b, {24,4,10}*1920b, {6,4,40}*1920b, {12,4,10}*1920a, {6,4,20}*1920a, {6,16,10}*1920, {6,4,10}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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