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Polytope of Type {4,16,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,16,2}*256a
if this polytope has a name.
Group : SmallGroup(256,26498)
Rank : 4
Schlafli Type : {4,16,2}
Number of vertices, edges, etc : 4, 32, 16, 2
Order of s0s1s2s3 : 16
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,16,2,2} of size 512
   {4,16,2,3} of size 768
   {4,16,2,5} of size 1280
   {4,16,2,7} of size 1792
Vertex Figure Of :
   {2,4,16,2} of size 512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,8,2}*128a, {2,16,2}*128
   4-fold quotients : {4,4,2}*64, {2,8,2}*64
   8-fold quotients : {2,4,2}*32, {4,2,2}*32
   16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,16,2}*512a, {8,16,2}*512c, {8,16,2}*512d, {4,16,4}*512a, {4,32,2}*512a, {4,32,2}*512b
   3-fold covers : {4,16,6}*768a, {12,16,2}*768a, {4,48,2}*768a
   5-fold covers : {4,16,10}*1280a, {20,16,2}*1280a, {4,80,2}*1280a
   7-fold covers : {4,16,14}*1792a, {28,16,2}*1792a, {4,112,2}*1792a
Permutation Representation (GAP) :
s0 := ( 1,17)( 2,18)( 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)(33,49)(34,50)(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);;
s1 := ( 3, 4)( 7, 8)( 9,11)(10,12)(13,15)(14,16)(17,21)(18,22)(19,24)(20,23)
(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,44)(36,43)(37,45)(38,46)(39,48)
(40,47)(49,61)(50,62)(51,64)(52,63)(53,57)(54,58)(55,60)(56,59);;
s2 := ( 1,33)( 2,34)( 3,36)( 4,35)( 5,37)( 6,38)( 7,40)( 8,39)( 9,43)(10,44)
(11,41)(12,42)(13,47)(14,48)(15,45)(16,46)(17,49)(18,50)(19,52)(20,51)(21,53)
(22,54)(23,56)(24,55)(25,59)(26,60)(27,57)(28,58)(29,63)(30,64)(31,61)
(32,62);;
s3 := (65,66);;
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(66)!( 1,17)( 2,18)( 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)(33,49)(34,50)(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);
s1 := Sym(66)!( 3, 4)( 7, 8)( 9,11)(10,12)(13,15)(14,16)(17,21)(18,22)(19,24)
(20,23)(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,44)(36,43)(37,45)(38,46)
(39,48)(40,47)(49,61)(50,62)(51,64)(52,63)(53,57)(54,58)(55,60)(56,59);
s2 := Sym(66)!( 1,33)( 2,34)( 3,36)( 4,35)( 5,37)( 6,38)( 7,40)( 8,39)( 9,43)
(10,44)(11,41)(12,42)(13,47)(14,48)(15,45)(16,46)(17,49)(18,50)(19,52)(20,51)
(21,53)(22,54)(23,56)(24,55)(25,59)(26,60)(27,57)(28,58)(29,63)(30,64)(31,61)
(32,62);
s3 := Sym(66)!(65,66);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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