Polytope of Type {12,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*1200
if this polytope has a name.
Group : SmallGroup(1200,961)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 150, 300, 50
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,4}*400
   6-fold quotients : {4,4}*200
   50-fold quotients : {6,2}*24
   100-fold quotients : {3,2}*12
   150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      25 facets:
         25 of {12}*24
      75 vertex figures:
         75 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      26 facets:
         2 of {6}*12
         24 of {12}*24
      78 vertex figures:
         72 of {4}*8
         6 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      25 facets:
         25 of {12}*24
      75 vertex figures:
         75 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      13 facets:
         1 of {6}*12
         12 of {12}*24
      39 vertex figures:
         36 of {4}*8
         3 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 5.
      10 facets:
         10 of {12}*24
      30 vertex figures:
         30 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 5.
      10 facets:
         10 of {12}*24
      30 vertex figures:
         30 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 10.
      5 facets:
         5 of {12}*24
      15 vertex figures:
         15 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 10.
      6 facets:
         2 of {6}*12
         4 of {12}*24
      18 vertex figures:
         12 of {4}*8
         6 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 10.
      6 facets:
         2 of {6}*12
         4 of {12}*24
      18 vertex figures:
         12 of {4}*8
         6 of {2}*4

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {12,4}

Twisty Puzzle