Polytope of Type {12,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*384b
if this polytope has a name.
Group : SmallGroup(384,1722)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 24, 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
Facet Of :
   {12,8,2} of size 768
Vertex Figure Of :
   {2,12,8} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*192a
   3-fold quotients : {4,8}*128b
   4-fold quotients : {12,4}*96a
   6-fold quotients : {4,4}*64
   8-fold quotients : {12,2}*48, {6,4}*48a
   12-fold quotients : {4,4}*32
   16-fold quotients : {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}*768a, {24,8}*768b, {24,8}*768d, {12,8}*768b, {12,8}*768d, {24,8}*768f, {24,8}*768h
   3-fold covers : {36,8}*1152b, {12,24}*1152d, {12,24}*1152e
   5-fold covers : {60,8}*1920b, {12,40}*1920b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      8 facets:
         8 of {12}*24
      12 vertex figures:
         12 of {8}*16

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {12,8}

Twisty Puzzle