Polytope of Type {16,4}

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

s0 := ( 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);;
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 := ( 1,17)( 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);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := 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);
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)!( 1,17)( 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);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope