Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*384b
if this polytope has a name.
Group : SmallGroup(384,1722)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 16, 96, 24
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,12,2} of size 768
Vertex Figure Of :
   {2,8,12} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12}*192a
   3-fold quotients : {8,4}*128b
   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, {8,24}*768b, {8,24}*768d, {8,12}*768b, {8,12}*768d, {8,24}*768f, {8,24}*768h
   3-fold covers : {8,36}*1152b, {24,12}*1152d, {24,12}*1152e
   5-fold covers : {8,60}*1920b, {40,12}*1920b
Permutation Representation (GAP) :

s0 := ( 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);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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)!( 1,73)( 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);
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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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