Polytope of Type {15,6,2}

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

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

Permutation Representation (Magma) :

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

to this polytope