Polytope of Type {30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,238598)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 160, 480, 32
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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) :
   4-fold quotients : {30,6}*480
   5-fold quotients : {6,6}*384c
   8-fold quotients : {15,6}*240
   10-fold quotients : {6,6}*192a
   20-fold quotients : {6,6}*96
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,3}*24
   96-fold quotients : {5,2}*20
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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