Polytope of Type {10,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,30}*600a
if this polytope has a name.
Group : SmallGroup(600,174)
Rank : 3
Schlafli Type : {10,30}
Number of vertices, edges, etc : 10, 150, 30
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,30,2} of size 1200
Vertex Figure Of :
   {2,10,30} of size 1200
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,10}*200c
   5-fold quotients : {10,6}*120
   6-fold quotients : {5,10}*100
   15-fold quotients : {10,2}*40
   25-fold quotients : {2,6}*24
   30-fold quotients : {5,2}*20
   50-fold quotients : {2,3}*12
   75-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,30}*1200a, {10,60}*1200a
   3-fold covers : {10,90}*1800a, {30,30}*1800e, {30,30}*1800f
Permutation Representation (GAP) :

s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)
(14,18)(15,17)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,41)(37,45)
(38,44)(39,43)(40,42)(52,55)(53,54)(56,71)(57,75)(58,74)(59,73)(60,72)(61,66)
(62,70)(63,69)(64,68)(65,67);;
s1 := ( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,22)(12,21)(13,25)(14,24)(15,23)
(16,17)(18,20)(26,57)(27,56)(28,60)(29,59)(30,58)(31,52)(32,51)(33,55)(34,54)
(35,53)(36,72)(37,71)(38,75)(39,74)(40,73)(41,67)(42,66)(43,70)(44,69)(45,68)
(46,62)(47,61)(48,65)(49,64)(50,63);;
s2 := ( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,31)( 7,35)( 8,34)( 9,33)(10,32)
(11,36)(12,40)(13,39)(14,38)(15,37)(16,41)(17,45)(18,44)(19,43)(20,42)(21,46)
(22,50)(23,49)(24,48)(25,47)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)
(68,69)(72,75)(73,74);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(75)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)
(13,19)(14,18)(15,17)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,41)
(37,45)(38,44)(39,43)(40,42)(52,55)(53,54)(56,71)(57,75)(58,74)(59,73)(60,72)
(61,66)(62,70)(63,69)(64,68)(65,67);
s1 := Sym(75)!( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,22)(12,21)(13,25)(14,24)
(15,23)(16,17)(18,20)(26,57)(27,56)(28,60)(29,59)(30,58)(31,52)(32,51)(33,55)
(34,54)(35,53)(36,72)(37,71)(38,75)(39,74)(40,73)(41,67)(42,66)(43,70)(44,69)
(45,68)(46,62)(47,61)(48,65)(49,64)(50,63);
s2 := Sym(75)!( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,31)( 7,35)( 8,34)( 9,33)
(10,32)(11,36)(12,40)(13,39)(14,38)(15,37)(16,41)(17,45)(18,44)(19,43)(20,42)
(21,46)(22,50)(23,49)(24,48)(25,47)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)
(67,70)(68,69)(72,75)(73,74);
poly := sub<Sym(75)|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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope