Polytope of Type {8,30,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239473)
Rank : 4
Schlafli Type : {8,30,2}
Number of vertices, edges, etc : 16, 240, 60, 2
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 : {4,30,2}*480c
   5-fold quotients : {8,6,2}*384a
   8-fold quotients : {4,15,2}*240
   20-fold quotients : {4,6,2}*96b
   40-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope