Polytope of Type {6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*192b
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 12, 48, 16
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,8,2} of size 384
   {6,8,4} of size 768
   {6,8,6} of size 1152
   {6,8,10} of size 1920
Vertex Figure Of :
   {2,6,8} of size 384
   {4,6,8} of size 768
   {4,6,8} of size 768
   {4,6,8} of size 768
   {6,6,8} of size 1152
   {6,6,8} of size 1152
   {6,6,8} of size 1728
   {10,6,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,8}*96, {6,4}*96
   4-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   8-fold quotients : {3,4}*24, {6,2}*24
   16-fold quotients : {3,2}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8}*384e, {6,8}*384f, {12,8}*384h
   3-fold covers : {18,8}*576b, {6,24}*576b, {6,24}*576e
   4-fold covers : {6,8}*768d, {6,8}*768e, {6,8}*768f, {24,8}*768i, {24,8}*768j, {6,8}*768j, {24,8}*768n, {12,8}*768p, {24,8}*768p, {12,8}*768s
   5-fold covers : {6,40}*960e, {30,8}*960b
   6-fold covers : {36,8}*1152e, {18,8}*1152f, {36,8}*1152h, {12,24}*1152k, {12,24}*1152l, {12,24}*1152m, {6,24}*1152d, {6,24}*1152l, {12,24}*1152v
   7-fold covers : {6,56}*1344c, {42,8}*1344b
   9-fold covers : {54,8}*1728b, {6,72}*1728c, {18,24}*1728b, {6,24}*1728b, {18,24}*1728e, {6,24}*1728e, {6,24}*1728f
   10-fold covers : {12,40}*1920f, {6,40}*1920b, {12,40}*1920h, {60,8}*1920e, {30,8}*1920f, {60,8}*1920h
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope