Polytope of Type {2,30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239472)
Rank : 4
Schlafli Type : {2,30,4}
Number of vertices, edges, etc : 2, 120, 240, 16
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {2,30,4}*480b
   5-fold quotients : {2,6,4}*384a
   8-fold quotients : {2,15,4}*240
   20-fold quotients : {2,6,4}*96c
   40-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,67)(20,68)(21,70)(22,69)
(23,75)(24,76)(25,78)(26,77)(27,71)(28,72)(29,74)(30,73)(31,79)(32,80)(33,82)
(34,81)(35,51)(36,52)(37,54)(38,53)(39,59)(40,60)(41,62)(42,61)(43,55)(44,56)
(45,58)(46,57)(47,63)(48,64)(49,66)(50,65);;
s2 := ( 3,19)( 4,22)( 5,21)( 6,20)( 7,25)( 8,24)( 9,23)(10,26)(11,32)(12,33)
(13,34)(14,31)(15,30)(16,27)(17,28)(18,29)(35,67)(36,70)(37,69)(38,68)(39,73)
(40,72)(41,71)(42,74)(43,80)(44,81)(45,82)(46,79)(47,78)(48,75)(49,76)(50,77)
(52,54)(55,57)(59,64)(60,65)(61,66)(62,63);;
s3 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,11)( 8,12)( 9,13)(10,14)(19,31)(20,32)
(21,33)(22,34)(23,27)(24,28)(25,29)(26,30)(35,47)(36,48)(37,49)(38,50)(39,43)
(40,44)(41,45)(42,46)(51,63)(52,64)(53,65)(54,66)(55,59)(56,60)(57,61)(58,62)
(67,79)(68,80)(69,81)(70,82)(71,75)(72,76)(73,77)(74,78);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(82)!(1,2);
s1 := Sym(82)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,67)(20,68)(21,70)
(22,69)(23,75)(24,76)(25,78)(26,77)(27,71)(28,72)(29,74)(30,73)(31,79)(32,80)
(33,82)(34,81)(35,51)(36,52)(37,54)(38,53)(39,59)(40,60)(41,62)(42,61)(43,55)
(44,56)(45,58)(46,57)(47,63)(48,64)(49,66)(50,65);
s2 := Sym(82)!( 3,19)( 4,22)( 5,21)( 6,20)( 7,25)( 8,24)( 9,23)(10,26)(11,32)
(12,33)(13,34)(14,31)(15,30)(16,27)(17,28)(18,29)(35,67)(36,70)(37,69)(38,68)
(39,73)(40,72)(41,71)(42,74)(43,80)(44,81)(45,82)(46,79)(47,78)(48,75)(49,76)
(50,77)(52,54)(55,57)(59,64)(60,65)(61,66)(62,63);
s3 := Sym(82)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,11)( 8,12)( 9,13)(10,14)(19,31)
(20,32)(21,33)(22,34)(23,27)(24,28)(25,29)(26,30)(35,47)(36,48)(37,49)(38,50)
(39,43)(40,44)(41,45)(42,46)(51,63)(52,64)(53,65)(54,66)(55,59)(56,60)(57,61)
(58,62)(67,79)(68,80)(69,81)(70,82)(71,75)(72,76)(73,77)(74,78);
poly := sub<Sym(82)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope