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Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*360a
if this polytope has a name.
Group : SmallGroup(360,137)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 30, 90, 6
Order of s0s1s2 : 30
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {30,6,2} of size 720
   {30,6,4} of size 1440
   {30,6,4} of size 1440
Vertex Figure Of :
   {2,30,6} of size 720
   {4,30,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,6}*120
   5-fold quotients : {6,6}*72b
   9-fold quotients : {10,2}*40
   10-fold quotients : {6,3}*36
   15-fold quotients : {2,6}*24
   18-fold quotients : {5,2}*20
   30-fold quotients : {2,3}*12
   45-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,6}*720a, {30,12}*720a
   3-fold covers : {30,18}*1080a, {30,6}*1080a, {30,6}*1080d
   4-fold covers : {120,6}*1440a, {30,24}*1440a, {60,12}*1440a, {30,6}*1440g, {60,6}*1440c
   5-fold covers : {150,6}*1800a, {30,30}*1800c, {30,30}*1800e
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6,11)( 7,15)( 8,14)( 9,13)(10,12)(17,20)(18,19)(21,26)
(22,30)(23,29)(24,28)(25,27)(32,35)(33,34)(36,41)(37,45)(38,44)(39,43)
(40,42);;
s1 := ( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,37)(17,36)(18,40)
(19,39)(20,38)(21,32)(22,31)(23,35)(24,34)(25,33)(26,42)(27,41)(28,45)(29,44)
(30,43);;
s2 := ( 1,16)( 2,17)( 3,18)( 4,19)( 5,20)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)
(11,21)(12,22)(13,23)(14,24)(15,25)(36,41)(37,42)(38,43)(39,44)(40,45);;
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, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(45)!( 2, 5)( 3, 4)( 6,11)( 7,15)( 8,14)( 9,13)(10,12)(17,20)(18,19)
(21,26)(22,30)(23,29)(24,28)(25,27)(32,35)(33,34)(36,41)(37,45)(38,44)(39,43)
(40,42);
s1 := Sym(45)!( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,37)(17,36)
(18,40)(19,39)(20,38)(21,32)(22,31)(23,35)(24,34)(25,33)(26,42)(27,41)(28,45)
(29,44)(30,43);
s2 := Sym(45)!( 1,16)( 2,17)( 3,18)( 4,19)( 5,20)( 6,26)( 7,27)( 8,28)( 9,29)
(10,30)(11,21)(12,22)(13,23)(14,24)(15,25)(36,41)(37,42)(38,43)(39,44)(40,45);
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, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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