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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6,3}*720
if this polytope has a name.
Group : SmallGroup(720,813)
Rank : 5
Schlafli Type : {2,10,6,3}
Number of vertices, edges, etc : 2, 10, 30, 9, 3
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,6,3,2} of size 1440
Vertex Figure Of :
   {2,2,10,6,3} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,10,2,3}*240
   5-fold quotients : {2,2,6,3}*144
   6-fold quotients : {2,5,2,3}*120
   15-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,20,6,3}*1440, {4,10,6,3}*1440, {2,10,6,6}*1440b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope