Polytope of Type {30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4}*960a
if this polytope has a name.
Group : SmallGroup(960,6310)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 120, 240, 16
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {30,4,2} of size 1920
Vertex Figure Of :
   {2,30,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {30,4}*240b
   5-fold quotients : {6,4}*192a
   8-fold quotients : {15,4}*120
   20-fold quotients : {6,4}*48c
   40-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,4}*1920b, {60,4}*1920c, {30,8}*1920b, {30,8}*1920c, {30,4}*1920a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope