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}*384a
if this polytope has a name.
Group : SmallGroup(384,1706)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 16, 96, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
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}*192a
   3-fold quotients : {4,4}*128
   4-fold quotients : {4,12}*96a
   6-fold quotients : {4,4}*64
   8-fold quotients : {2,12}*48, {4,6}*48a
   12-fold quotients : {4,4}*32
   16-fold quotients : {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}*768a, {4,24}*768a, {4,12}*768a, {8,12}*768c, {4,24}*768c
   3-fold covers : {4,36}*1152a, {12,12}*1152b, {12,12}*1152c
   5-fold covers : {4,60}*1920a, {20,12}*1920a
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1> of order 2.
      30 facets:
         12 of {2}*4
         18 of {4}*8
      8 vertex figures:
         8 of {12}*24
   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=<s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*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*s0*s2*s1*s0*s2*s1*s0*s2*s1> 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*s1*s2*s1*s2> of order 2.
      24 facets:
         24 of {4}*8
      10 vertex figures:
         4 of {6}*12
         6 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      15 facets:
         6 of {2}*4
         9 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      12 facets:
         12 of {4}*8
      6 vertex figures:
         4 of {6}*12
         2 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*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, s1*s0*s1*s2*s1*s0*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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      18 facets:
         12 of {2}*4
         6 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
      12 facets:
         12 of {4}*8
      5 vertex figures:
         2 of {6}*12
         3 of {12}*24

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