Polytope of Type {2,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16}*64
if this polytope has a name.
Group : SmallGroup(64,186)
Rank : 3
Schlafli Type : {2,16}
Number of vertices, edges, etc : 2, 16, 16
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,16,2} of size 128
   {2,16,4} of size 256
   {2,16,4} of size 256
   {2,16,6} of size 384
   {2,16,4} of size 512
   {2,16,4} of size 512
   {2,16,8} of size 512
   {2,16,8} of size 512
   {2,16,8} of size 512
   {2,16,8} of size 512
   {2,16,8} of size 512
   {2,16,8} of size 512
   {2,16,10} of size 640
   {2,16,12} of size 768
   {2,16,12} of size 768
   {2,16,14} of size 896
   {2,16,18} of size 1152
   {2,16,6} of size 1152
   {2,16,20} of size 1280
   {2,16,20} of size 1280
   {2,16,22} of size 1408
   {2,16,26} of size 1664
   {2,16,28} of size 1792
   {2,16,28} of size 1792
   {2,16,30} of size 1920
Vertex Figure Of :
   {2,2,16} of size 128
   {3,2,16} of size 192
   {4,2,16} of size 256
   {5,2,16} of size 320
   {6,2,16} of size 384
   {7,2,16} of size 448
   {9,2,16} of size 576
   {10,2,16} of size 640
   {11,2,16} of size 704
   {12,2,16} of size 768
   {13,2,16} of size 832
   {14,2,16} of size 896
   {15,2,16} of size 960
   {17,2,16} of size 1088
   {18,2,16} of size 1152
   {19,2,16} of size 1216
   {20,2,16} of size 1280
   {21,2,16} of size 1344
   {22,2,16} of size 1408
   {23,2,16} of size 1472
   {25,2,16} of size 1600
   {26,2,16} of size 1664
   {27,2,16} of size 1728
   {28,2,16} of size 1792
   {29,2,16} of size 1856
   {30,2,16} of size 1920
   {31,2,16} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,8}*32
   4-fold quotients : {2,4}*16
   8-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,16}*128a, {2,32}*128
   3-fold covers : {2,48}*192, {6,16}*192
   4-fold covers : {4,16}*256a, {8,16}*256c, {8,16}*256d, {4,32}*256a, {4,32}*256b, {2,64}*256
   5-fold covers : {2,80}*320, {10,16}*320
   6-fold covers : {4,48}*384a, {12,16}*384a, {2,96}*384, {6,32}*384
   7-fold covers : {2,112}*448, {14,16}*448
   8-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, {2,128}*512
   9-fold covers : {2,144}*576, {18,16}*576, {6,48}*576a, {6,48}*576b, {6,48}*576c, {6,16}*576
   10-fold covers : {4,80}*640a, {20,16}*640a, {2,160}*640, {10,32}*640
   11-fold covers : {2,176}*704, {22,16}*704
   12-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, {6,64}*768, {2,192}*768, {4,48}*768c, {6,16}*768b, {6,48}*768a
   13-fold covers : {2,208}*832, {26,16}*832
   14-fold covers : {4,112}*896a, {28,16}*896a, {2,224}*896, {14,32}*896
   15-fold covers : {10,48}*960, {6,80}*960, {2,240}*960, {30,16}*960
   17-fold covers : {34,16}*1088, {2,272}*1088
   18-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, {18,32}*1152, {2,288}*1152, {6,96}*1152a, {6,96}*1152b, {6,96}*1152c, {6,32}*1152
   19-fold covers : {38,16}*1216, {2,304}*1216
   20-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, {10,64}*1280, {2,320}*1280
   21-fold covers : {14,48}*1344, {6,112}*1344, {2,336}*1344, {42,16}*1344
   22-fold covers : {44,16}*1408a, {4,176}*1408a, {22,32}*1408, {2,352}*1408
   23-fold covers : {46,16}*1472, {2,368}*1472
   25-fold covers : {2,400}*1600, {50,16}*1600, {10,80}*1600a, {10,80}*1600b, {10,80}*1600c, {10,16}*1600
   26-fold covers : {52,16}*1664a, {4,208}*1664a, {26,32}*1664, {2,416}*1664
   27-fold covers : {2,432}*1728, {54,16}*1728, {6,144}*1728a, {6,144}*1728b, {18,48}*1728a, {6,48}*1728a, {6,48}*1728b, {18,48}*1728b, {6,48}*1728c, {6,16}*1728a, {6,48}*1728d, {6,48}*1728e, {6,48}*1728f, {6,16}*1728b, {6,48}*1728g, {6,48}*1728h
   28-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, {14,64}*1792, {2,448}*1792
   29-fold covers : {58,16}*1856, {2,464}*1856
   30-fold covers : {60,16}*1920a, {4,240}*1920a, {12,80}*1920a, {20,48}*1920a, {30,32}*1920, {2,480}*1920, {10,96}*1920, {6,160}*1920
   31-fold covers : {62,16}*1984, {2,496}*1984
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
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*s1*s0*s1, s0*s2*s0*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!(1,2);
s1 := Sym(18)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s2 := Sym(18)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
poly := sub<Sym(18)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

to this polytope