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}*384d
if this polytope has a name.
Group : SmallGroup(384,17873)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 48, 96, 16
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {12,4,2} of size 768
Vertex Figure Of :
   {2,12,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*192b, {6,4}*192b, {12,4}*192c
   4-fold quotients : {12,4}*96a, {12,4}*96b, {12,4}*96c, {6,4}*96
   8-fold quotients : {12,2}*48, {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   12-fold quotients : {4,4}*32
   16-fold quotients : {3,4}*24, {6,2}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8}*768s, {24,4}*768i, {12,4}*768d, {12,8}*768t, {24,4}*768j, {12,8}*768u, {12,4}*768e, {24,4}*768k, {12,8}*768w, {12,4}*768f, {24,4}*768l
   3-fold covers : {36,4}*1152d, {12,12}*1152k, {12,12}*1152m
   5-fold covers : {12,20}*1920c, {60,4}*1920d
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 2.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {12}*24
      32 vertex figures:
         16 of {2}*4
         16 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 2.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      8 facets:
         4 of {4}*8
         4 of {12}*24
      16 vertex figures:
         16 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1> of order 4.
      4 facets:
         4 of {12}*24
      20 vertex figures:
         4 of {4}*8
         16 of {2}*4
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8

Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)(72,92);;
s1 := ( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)(11,60)(12,59)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,69)(22,70)(23,72)(24,71)(25,77)(26,78)(27,80)(28,79)(29,73)(30,74)(31,76)(32,75)(33,81)(34,82)(35,84)(36,83)(37,89)(38,90)(39,92)(40,91)(41,85)(42,86)(43,88)(44,87)(45,93)(46,94)(47,96)(48,95);;
s2 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,64)(50,63)(51,62)(52,61)(53,68)(54,67)(55,66)(56,65)(57,72)(58,71)(59,70)(60,69)(73,88)(74,87)(75,86)(76,85)(77,92)(78,91)(79,90)(80,89)(81,96)(82,95)(83,94)(84,93);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*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*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)(72,92);
s1 := Sym(96)!( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)(11,60)(12,59)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,69)(22,70)(23,72)(24,71)(25,77)(26,78)(27,80)(28,79)(29,73)(30,74)(31,76)(32,75)(33,81)(34,82)(35,84)(36,83)(37,89)(38,90)(39,92)(40,91)(41,85)(42,86)(43,88)(44,87)(45,93)(46,94)(47,96)(48,95);
s2 := Sym(96)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,64)(50,63)(51,62)(52,61)(53,68)(54,67)(55,66)(56,65)(57,72)(58,71)(59,70)(60,69)(73,88)(74,87)(75,86)(76,85)(77,92)(78,91)(79,90)(80,89)(81,96)(82,95)(83,94)(84,93);
poly := sub<Sym(96)|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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*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*s0*s1*s0*s1 >;

References : None.
to this polytope

Polytope of Type {12,4}

Twisty Puzzle