Polytope of Type {2,3,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,10}*720
if this polytope has a name.
Group : SmallGroup(720,813)
Rank : 5
Schlafli Type : {2,3,6,10}
Number of vertices, edges, etc : 2, 3, 9, 30, 10
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,6,10,2} of size 1440
Vertex Figure Of :
   {2,2,3,6,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,3,2,10}*240
   5-fold quotients : {2,3,6,2}*144
   6-fold quotients : {2,3,2,5}*120
   15-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,6,20}*1440, {2,6,6,10}*1440c
Permutation Representation (GAP) :

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

to this polytope