Polytope of Type {2,4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,30}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239472)
Rank : 4
Schlafli Type : {2,4,30}
Number of vertices, edges, etc : 2, 16, 240, 120
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 : {2,4,30}*480b
   5-fold quotients : {2,4,6}*384a
   8-fold quotients : {2,4,15}*240
   20-fold quotients : {2,4,6}*96c
   40-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope