Polytope of Type {2,8,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,30}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239473)
Rank : 4
Schlafli Type : {2,8,30}
Number of vertices, edges, etc : 2, 16, 240, 60
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}*480c
   5-fold quotients : {2,8,6}*384a
   8-fold quotients : {2,4,15}*240
   20-fold quotients : {2,4,6}*96b
   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)( 7,18)( 8,17)( 9,16)(10,15)(19,27)(20,28)
(21,29)(22,30)(23,34)(24,33)(25,32)(26,31)(35,43)(36,44)(37,45)(38,46)(39,50)
(40,49)(41,48)(42,47)(51,59)(52,60)(53,61)(54,62)(55,66)(56,65)(57,64)(58,63)
(67,75)(68,76)(69,77)(70,78)(71,82)(72,81)(73,80)(74,79);;
s2 := ( 5, 6)( 7,12)( 8,11)( 9,13)(10,14)(17,18)(19,67)(20,68)(21,70)(22,69)
(23,76)(24,75)(25,77)(26,78)(27,72)(28,71)(29,73)(30,74)(31,79)(32,80)(33,82)
(34,81)(35,51)(36,52)(37,54)(38,53)(39,60)(40,59)(41,61)(42,62)(43,56)(44,55)
(45,57)(46,58)(47,63)(48,64)(49,66)(50,65);;
s3 := ( 3,19)( 4,22)( 5,21)( 6,20)( 7,32)( 8,33)( 9,34)(10,31)(11,27)(12,30)
(13,29)(14,28)(15,26)(16,23)(17,24)(18,25)(35,67)(36,70)(37,69)(38,68)(39,80)
(40,81)(41,82)(42,79)(43,75)(44,78)(45,77)(46,76)(47,74)(48,71)(49,72)(50,73)
(52,54)(55,64)(56,65)(57,66)(58,63)(60,62);;
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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*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*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*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)( 7,18)( 8,17)( 9,16)(10,15)(19,27)
(20,28)(21,29)(22,30)(23,34)(24,33)(25,32)(26,31)(35,43)(36,44)(37,45)(38,46)
(39,50)(40,49)(41,48)(42,47)(51,59)(52,60)(53,61)(54,62)(55,66)(56,65)(57,64)
(58,63)(67,75)(68,76)(69,77)(70,78)(71,82)(72,81)(73,80)(74,79);
s2 := Sym(82)!( 5, 6)( 7,12)( 8,11)( 9,13)(10,14)(17,18)(19,67)(20,68)(21,70)
(22,69)(23,76)(24,75)(25,77)(26,78)(27,72)(28,71)(29,73)(30,74)(31,79)(32,80)
(33,82)(34,81)(35,51)(36,52)(37,54)(38,53)(39,60)(40,59)(41,61)(42,62)(43,56)
(44,55)(45,57)(46,58)(47,63)(48,64)(49,66)(50,65);
s3 := Sym(82)!( 3,19)( 4,22)( 5,21)( 6,20)( 7,32)( 8,33)( 9,34)(10,31)(11,27)
(12,30)(13,29)(14,28)(15,26)(16,23)(17,24)(18,25)(35,67)(36,70)(37,69)(38,68)
(39,80)(40,81)(41,82)(42,79)(43,75)(44,78)(45,77)(46,76)(47,74)(48,71)(49,72)
(50,73)(52,54)(55,64)(56,65)(57,66)(58,63)(60,62);
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, s3*s1*s2*s3*s1*s2*s1*s2*s3*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*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope