Polytope of Type {20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6}*360
if this polytope has a name.
Group : SmallGroup(360,134)
Rank : 3
Schlafli Type : {20,6}
Number of vertices, edges, etc : 30, 90, 9
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {20,6,2} of size 720
Vertex Figure Of :
   {2,20,6} of size 720
   {4,20,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {4,6}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,6}*720
   3-fold covers : {20,6}*1080, {60,6}*1080a, {60,6}*1080b, {60,6}*1080c
   4-fold covers : {40,6}*1440, {20,12}*1440
   5-fold covers : {100,6}*1800
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2 >;

References : None.
to this polytope