Polytope of Type {6,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3}*900
Also Known As : {6,3}(5,5). if this polytope has another name.
Group : SmallGroup(900,95)
Rank : 3
Schlafli Type : {6,3}
Number of vertices, edges, etc : 150, 225, 75
Order of s0s1s2 : 30
Order of s0s1s2s1 : 6
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,3,2} of size 1800
Vertex Figure Of :
   {2,6,3} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,3}*300
   25-fold quotients : {6,3}*36
   75-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,6}*1800c
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1> of order 3.
      27 facets:
         3 of {2}*4
         24 of {6}*12
      50 vertex figures:
         50 of {3}*6
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 5.
      15 facets:
         15 of {6}*12
      30 vertex figures:
         30 of {3}*6
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 5.
      15 facets:
         15 of {6}*12
      30 vertex figures:
         30 of {3}*6

Permutation Representation (GAP) : 
s0 := ( 2,24)( 3,17)( 4,15)( 5, 8)( 6,14)( 9,23)(10,16)(11,22)(12,20)(18,21)(27,49)(28,42)(29,40)(30,33)(31,39)(34,48)(35,41)(36,47)(37,45)(43,46)(52,74)(53,67)(54,65)(55,58)(56,64)(59,73)(60,66)(61,72)(62,70)(68,71);;
s1 := ( 2, 5)( 3, 4)( 6, 9)( 7, 8)(11,12)(13,15)(16,20)(17,19)(21,23)(24,25)(26,51)(27,55)(28,54)(29,53)(30,52)(31,59)(32,58)(33,57)(34,56)(35,60)(36,62)(37,61)(38,65)(39,64)(40,63)(41,70)(42,69)(43,68)(44,67)(45,66)(46,73)(47,72)(48,71)(49,75)(50,74);;
s2 := ( 1,32)( 2,39)( 3,41)( 4,48)( 5,30)( 6,49)( 7,26)( 8,33)( 9,40)(10,42)(11,36)(12,43)(13,50)(14,27)(15,34)(16,28)(17,35)(18,37)(19,44)(20,46)(21,45)(22,47)(23,29)(24,31)(25,38)(51,57)(52,64)(53,66)(54,73)(56,74)(59,65)(60,67)(62,68)(63,75)(70,71);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(75)!( 2,24)( 3,17)( 4,15)( 5, 8)( 6,14)( 9,23)(10,16)(11,22)(12,20)(18,21)(27,49)(28,42)(29,40)(30,33)(31,39)(34,48)(35,41)(36,47)(37,45)(43,46)(52,74)(53,67)(54,65)(55,58)(56,64)(59,73)(60,66)(61,72)(62,70)(68,71);
s1 := Sym(75)!( 2, 5)( 3, 4)( 6, 9)( 7, 8)(11,12)(13,15)(16,20)(17,19)(21,23)(24,25)(26,51)(27,55)(28,54)(29,53)(30,52)(31,59)(32,58)(33,57)(34,56)(35,60)(36,62)(37,61)(38,65)(39,64)(40,63)(41,70)(42,69)(43,68)(44,67)(45,66)(46,73)(47,72)(48,71)(49,75)(50,74);
s2 := Sym(75)!( 1,32)( 2,39)( 3,41)( 4,48)( 5,30)( 6,49)( 7,26)( 8,33)( 9,40)(10,42)(11,36)(12,43)(13,50)(14,27)(15,34)(16,28)(17,35)(18,37)(19,44)(20,46)(21,45)(22,47)(23,29)(24,31)(25,38)(51,57)(52,64)(53,66)(54,73)(56,74)(59,65)(60,67)(62,68)(63,75)(70,71);
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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;
References : None.
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