Polytope of Type {16,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,24}*768a
if this polytope has a name.
Group : SmallGroup(768,82963)
Rank : 3
Schlafli Type : {16,24}
Number of vertices, edges, etc : 16, 192, 24
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 : {8,24}*384a
   3-fold quotients : {16,8}*256a
   4-fold quotients : {4,24}*192a, {8,12}*192b
   6-fold quotients : {8,8}*128a
   8-fold quotients : {4,12}*96a, {2,24}*96
   12-fold quotients : {4,8}*64a, {8,4}*64b
   16-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {4,4}*32, {2,8}*32
   32-fold quotients : {2,6}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {2,3}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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