Polytope of Type {48,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,8}*768b
if this polytope has a name.
Group : SmallGroup(768,82982)
Rank : 3
Schlafli Type : {48,8}
Number of vertices, edges, etc : 48, 192, 8
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,8}*384d
   3-fold quotients : {16,8}*256b
   4-fold quotients : {24,4}*192b, {12,8}*192a
   6-fold quotients : {8,8}*128a
   8-fold quotients : {12,4}*96a, {6,8}*96
   12-fold quotients : {4,8}*64a, {8,4}*64b
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*32, {2,8}*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 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,34)( 8,36)( 9,35)(10,31)
(11,33)(12,32)(13,46)(14,48)(15,47)(16,43)(17,45)(18,44)(19,40)(20,42)(21,41)
(22,37)(23,39)(24,38)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)(56,84)
(57,83)(58,79)(59,81)(60,80)(61,94)(62,96)(63,95)(64,91)(65,93)(66,92)(67,88)
(68,90)(69,89)(70,85)(71,87)(72,86);;
s1 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,23)(14,22)(15,24)(16,20)(17,19)
(18,21)(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)(61,71)(62,70)(63,72)(64,68)
(65,67)(66,69)(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 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,58)( 8,59)( 9,60)(10,55)
(11,56)(12,57)(13,67)(14,68)(15,69)(16,70)(17,71)(18,72)(19,61)(20,62)(21,63)
(22,64)(23,65)(24,66)(25,73)(26,74)(27,75)(28,76)(29,77)(30,78)(31,82)(32,83)
(33,84)(34,79)(35,80)(36,81)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)
(44,86)(45,87)(46,88)(47,89)(48,90);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope