Polytope of Type {2,15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,238293)
Rank : 4
Schlafli Type : {2,15,6}
Number of vertices, edges, etc : 2, 80, 240, 32
Order of s₀s₁s₂s₃ : 40
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 : {2,15,6}*480
   5-fold quotients : {2,3,6}*384
   20-fold quotients : {2,3,6}*96
   40-fold quotients : {2,3,3}*48
   48-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope