Polytope of Type {2,8,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,15}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239473)
Rank : 4
Schlafli Type : {2,8,15}
Number of vertices, edges, etc : 2, 32, 240, 60
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,4,15}*480
   5-fold quotients : {2,8,3}*384
   8-fold quotients : {2,4,15}*240
   16-fold quotients : {2,2,15}*120
   20-fold quotients : {2,4,3}*96
   40-fold quotients : {2,4,3}*48
   48-fold quotients : {2,2,5}*40
   80-fold quotients : {2,2,3}*24
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 := ( 3,27)( 4,30)( 5,29)( 6,28)( 7,25)( 8,24)( 9,23)(10,26)(11,19)(12,22)
(13,21)(14,20)(15,31)(16,34)(17,33)(18,32)(35,75)(36,78)(37,77)(38,76)(39,73)
(40,72)(41,71)(42,74)(43,67)(44,70)(45,69)(46,68)(47,79)(48,82)(49,81)(50,80)
(51,59)(52,62)(53,61)(54,60)(55,57)(64,66);;
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*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 ];;
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)!( 3,27)( 4,30)( 5,29)( 6,28)( 7,25)( 8,24)( 9,23)(10,26)(11,19)
(12,22)(13,21)(14,20)(15,31)(16,34)(17,33)(18,32)(35,75)(36,78)(37,77)(38,76)
(39,73)(40,72)(41,71)(42,74)(43,67)(44,70)(45,69)(46,68)(47,79)(48,82)(49,81)
(50,80)(51,59)(52,62)(53,61)(54,60)(55,57)(64,66);
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*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 >;

to this polytope