Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240800)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 120, 480, 80
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,8}*960b, {12,4}*960b
   4-fold quotients : {12,4}*480a, {12,4}*480b, {6,4}*480
   8-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   16-fold quotients : {6,4}*120
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope