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

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

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

to this polytope