Polytope of Type {2,6,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,10}*960
if this polytope has a name.
Group : SmallGroup(960,11219)
Rank : 5
Schlafli Type : {2,6,4,10}
Number of vertices, edges, etc : 2, 6, 12, 20, 10
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,4,10,2} of size 1920
Vertex Figure Of :
   {2,2,6,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,2,10}*480
   3-fold quotients : {2,2,4,10}*320
   4-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
   5-fold quotients : {2,6,4,2}*192a
   6-fold quotients : {2,2,2,10}*160
   8-fold quotients : {2,3,2,5}*120
   10-fold quotients : {2,6,2,2}*96
   12-fold quotients : {2,2,2,5}*80
   15-fold quotients : {2,2,4,2}*64
   20-fold quotients : {2,3,2,2}*48
   30-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,4,10}*1920, {2,6,4,20}*1920, {4,6,4,10}*1920a, {2,6,8,10}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope