Polytope of Type {24,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,16}*768b
if this polytope has a name.
Group : SmallGroup(768,82983)
Rank : 3
Schlafli Type : {24,16}
Number of vertices, edges, etc : 24, 192, 16
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,8}*384a
   3-fold quotients : {8,16}*256b
   4-fold quotients : {24,4}*192a, {12,8}*192b
   6-fold quotients : {8,8}*128c
   8-fold quotients : {12,4}*96a, {24,2}*96
   12-fold quotients : {8,4}*64a, {4,8}*64b
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*32, {8,2}*32
   32-fold quotients : {6,2}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {3,2}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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