Polytope of Type {4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,16}*128a
Also Known As : {4,16|2}. if this polytope has another name.
Group : SmallGroup(128,916)
Rank : 3
Schlafli Type : {4,16}
Number of vertices, edges, etc : 4, 32, 16
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,16,2} of size 256
   {4,16,4} of size 512
   {4,16,4} of size 512
   {4,16,6} of size 768
   {4,16,10} of size 1280
   {4,16,14} of size 1792
Vertex Figure Of :
   {2,4,16} of size 256
   {4,4,16} of size 512
   {6,4,16} of size 768
   {3,4,16} of size 768
   {6,4,16} of size 1152
   {10,4,16} of size 1280
   {14,4,16} of size 1792
   {5,4,16} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,8}*64a, {2,16}*64
   4-fold quotients : {4,4}*32, {2,8}*32
   8-fold quotients : {2,4}*16, {4,2}*16
   16-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,16}*256a, {8,16}*256c, {8,16}*256d, {4,32}*256a, {4,32}*256b
   3-fold covers : {4,48}*384a, {12,16}*384a
   4-fold covers : {4,16}*512a, {8,16}*512a, {16,16}*512a, {16,16}*512b, {16,16}*512g, {16,16}*512h, {8,16}*512c, {4,32}*512a, {4,32}*512b, {8,32}*512a, {8,32}*512b, {8,32}*512c, {8,32}*512d, {4,64}*512a, {4,64}*512b
   5-fold covers : {4,80}*640a, {20,16}*640a
   6-fold covers : {12,16}*768a, {4,48}*768a, {24,16}*768c, {8,48}*768c, {8,48}*768d, {24,16}*768d, {12,32}*768a, {4,96}*768a, {12,32}*768b, {4,96}*768b
   7-fold covers : {4,112}*896a, {28,16}*896a
   9-fold covers : {36,16}*1152a, {4,144}*1152a, {12,48}*1152a, {12,48}*1152b, {12,48}*1152c, {4,16}*1152a, {4,48}*1152a, {12,16}*1152a
   10-fold covers : {20,16}*1280a, {4,80}*1280a, {40,16}*1280c, {8,80}*1280c, {8,80}*1280d, {40,16}*1280d, {20,32}*1280a, {4,160}*1280a, {20,32}*1280b, {4,160}*1280b
   11-fold covers : {44,16}*1408a, {4,176}*1408a
   13-fold covers : {52,16}*1664a, {4,208}*1664a
   14-fold covers : {28,16}*1792a, {4,112}*1792a, {56,16}*1792c, {8,112}*1792c, {8,112}*1792d, {56,16}*1792d, {28,32}*1792a, {4,224}*1792a, {28,32}*1792b, {4,224}*1792b
   15-fold covers : {60,16}*1920a, {4,240}*1920a, {12,80}*1920a, {20,48}*1920a
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(64)!( 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(64)!( 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(64)!( 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);
poly := sub<Sym(64)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope