Polytope of Type {2,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,16}*256a
if this polytope has a name.
Group : SmallGroup(256,26498)
Rank : 4
Schlafli Type : {2,4,16}
Number of vertices, edges, etc : 2, 4, 32, 16
Order of s₀s₁s₂s₃ : 16
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,16,2} of size 512
Vertex Figure Of :
   {2,2,4,16} of size 512
   {3,2,4,16} of size 768
   {5,2,4,16} of size 1280
   {7,2,4,16} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,8}*128a, {2,2,16}*128
   4-fold quotients : {2,4,4}*64, {2,2,8}*64
   8-fold quotients : {2,2,4}*32, {2,4,2}*32
   16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,16}*512a, {2,8,16}*512c, {2,8,16}*512d, {4,4,16}*512a, {2,4,32}*512a, {2,4,32}*512b
   3-fold covers : {6,4,16}*768a, {2,12,16}*768a, {2,4,48}*768a
   5-fold covers : {10,4,16}*1280a, {2,20,16}*1280a, {2,4,80}*1280a
   7-fold covers : {14,4,16}*1792a, {2,28,16}*1792a, {2,4,112}*1792a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope