Polytope of Type {2,16,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,8}*512b
if this polytope has a name.
Group : SmallGroup(512,396070)
Rank : 4
Schlafli Type : {2,16,8}
Number of vertices, edges, etc : 2, 16, 64, 8
Order of s₀s₁s₂s₃ : 16
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) :
   2-fold quotients : {2,8,8}*256a
   4-fold quotients : {2,4,8}*128a, {2,8,4}*128b
   8-fold quotients : {2,4,4}*64, {2,2,8}*64
   16-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3,19)( 4,20)( 5,22)( 6,21)( 7,26)( 8,25)( 9,24)(10,23)(11,29)(12,30)
(13,27)(14,28)(15,31)(16,32)(17,34)(18,33)(35,51)(36,52)(37,54)(38,53)(39,58)
(40,57)(41,56)(42,55)(43,61)(44,62)(45,59)(46,60)(47,63)(48,64)(49,66)
(50,65);;
s2 := ( 5, 6)( 7,10)( 8, 9)(13,14)(15,18)(16,17)(19,23)(20,24)(21,26)(22,25)
(27,32)(28,31)(29,33)(30,34)(35,43)(36,44)(37,46)(38,45)(39,50)(40,49)(41,48)
(42,47)(51,65)(52,66)(53,63)(54,64)(55,61)(56,62)(57,59)(58,60);;
s3 := ( 3,35)( 4,36)( 5,38)( 6,37)( 7,41)( 8,42)( 9,39)(10,40)(11,43)(12,44)
(13,46)(14,45)(15,49)(16,50)(17,47)(18,48)(19,51)(20,52)(21,54)(22,53)(23,57)
(24,58)(25,55)(26,56)(27,60)(28,59)(29,61)(30,62)(31,66)(32,65)(33,64)
(34,63);;
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*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope