Polytope of Type {4,12}

Play with this polytope as a twisty puzzle

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

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {4,12}

Twisty Puzzle