Polytope of Type {6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,30}*360a
if this polytope has a name.
Group : SmallGroup(360,137)
Rank : 3
Schlafli Type : {6,30}
Number of vertices, edges, etc : 6, 90, 30
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,30,2} of size 720
   {6,30,4} of size 1440
Vertex Figure Of :
   {2,6,30} of size 720
   {4,6,30} of size 1440
   {4,6,30} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,10}*120
   5-fold quotients : {6,6}*72c
   9-fold quotients : {2,10}*40
   10-fold quotients : {3,6}*36
   15-fold quotients : {6,2}*24
   18-fold quotients : {2,5}*20
   30-fold quotients : {3,2}*12
   45-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,60}*720a, {12,30}*720a
   3-fold covers : {18,30}*1080a, {6,30}*1080a, {6,30}*1080d
   4-fold covers : {6,120}*1440a, {24,30}*1440a, {12,60}*1440a, {6,30}*1440g, {6,60}*1440c
   5-fold covers : {6,150}*1800a, {30,30}*1800a, {30,30}*1800b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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