Polytope of Type {2,2,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,16}*512a
if this polytope has a name.
Group : SmallGroup(512,7529996)
Rank : 5
Schlafli Type : {2,2,4,16}
Number of vertices, edges, etc : 2, 2, 4, 32, 16
Order of s₀s₁s₂s₃s₄ : 16
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,2,4,8}*256a, {2,2,2,16}*256
   4-fold quotients : {2,2,4,4}*128, {2,2,2,8}*128
   8-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   16-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,30)
(15,31)(16,32)(17,33)(18,34)(19,35)(20,36)(37,53)(38,54)(39,55)(40,56)(41,57)
(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)
(52,68);;
s3 := ( 7, 8)(11,12)(13,15)(14,16)(17,19)(18,20)(21,25)(22,26)(23,28)(24,27)
(29,35)(30,36)(31,33)(32,34)(37,45)(38,46)(39,48)(40,47)(41,49)(42,50)(43,52)
(44,51)(53,65)(54,66)(55,68)(56,67)(57,61)(58,62)(59,64)(60,63);;
s4 := ( 5,37)( 6,38)( 7,40)( 8,39)( 9,41)(10,42)(11,44)(12,43)(13,47)(14,48)
(15,45)(16,46)(17,51)(18,52)(19,49)(20,50)(21,53)(22,54)(23,56)(24,55)(25,57)
(26,58)(27,60)(28,59)(29,63)(30,64)(31,61)(32,62)(33,67)(34,68)(35,65)
(36,66);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(68)!(1,2);
s1 := Sym(68)!(3,4);
s2 := Sym(68)!( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)
(14,30)(15,31)(16,32)(17,33)(18,34)(19,35)(20,36)(37,53)(38,54)(39,55)(40,56)
(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)
(52,68);
s3 := Sym(68)!( 7, 8)(11,12)(13,15)(14,16)(17,19)(18,20)(21,25)(22,26)(23,28)
(24,27)(29,35)(30,36)(31,33)(32,34)(37,45)(38,46)(39,48)(40,47)(41,49)(42,50)
(43,52)(44,51)(53,65)(54,66)(55,68)(56,67)(57,61)(58,62)(59,64)(60,63);
s4 := Sym(68)!( 5,37)( 6,38)( 7,40)( 8,39)( 9,41)(10,42)(11,44)(12,43)(13,47)
(14,48)(15,45)(16,46)(17,51)(18,52)(19,49)(20,50)(21,53)(22,54)(23,56)(24,55)
(25,57)(26,58)(27,60)(28,59)(29,63)(30,64)(31,61)(32,62)(33,67)(34,68)(35,65)
(36,66);
poly := sub<Sym(68)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope