Polytope of Type {16,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,2}*64
if this polytope has a name.
Group : SmallGroup(64,186)
Rank : 3
Schlafli Type : {16,2}
Number of vertices, edges, etc : 16, 16, 2
Order of s0s1s2 : 16
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{16,2,2} of size 128
{16,2,3} of size 192
{16,2,4} of size 256
{16,2,5} of size 320
{16,2,6} of size 384
{16,2,7} of size 448
{16,2,9} of size 576
{16,2,10} of size 640
{16,2,11} of size 704
{16,2,12} of size 768
{16,2,13} of size 832
{16,2,14} of size 896
{16,2,15} of size 960
{16,2,17} of size 1088
{16,2,18} of size 1152
{16,2,19} of size 1216
{16,2,20} of size 1280
{16,2,21} of size 1344
{16,2,22} of size 1408
{16,2,23} of size 1472
{16,2,25} of size 1600
{16,2,26} of size 1664
{16,2,27} of size 1728
{16,2,28} of size 1792
{16,2,29} of size 1856
{16,2,30} of size 1920
{16,2,31} of size 1984
Vertex Figure Of :
{2,16,2} of size 128
{4,16,2} of size 256
{4,16,2} of size 256
{6,16,2} of size 384
{4,16,2} of size 512
{4,16,2} of size 512
{8,16,2} of size 512
{8,16,2} of size 512
{8,16,2} of size 512
{8,16,2} of size 512
{8,16,2} of size 512
{8,16,2} of size 512
{10,16,2} of size 640
{12,16,2} of size 768
{12,16,2} of size 768
{14,16,2} of size 896
{18,16,2} of size 1152
{6,16,2} of size 1152
{20,16,2} of size 1280
{20,16,2} of size 1280
{22,16,2} of size 1408
{26,16,2} of size 1664
{28,16,2} of size 1792
{28,16,2} of size 1792
{30,16,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,2}*32
4-fold quotients : {4,2}*16
8-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {16,4}*128a, {32,2}*128
3-fold covers : {48,2}*192, {16,6}*192
4-fold covers : {16,4}*256a, {16,8}*256c, {16,8}*256d, {32,4}*256a, {32,4}*256b, {64,2}*256
5-fold covers : {80,2}*320, {16,10}*320
6-fold covers : {48,4}*384a, {16,12}*384a, {96,2}*384, {32,6}*384
7-fold covers : {112,2}*448, {16,14}*448
8-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, {128,2}*512
9-fold covers : {144,2}*576, {16,18}*576, {48,6}*576a, {48,6}*576b, {48,6}*576c, {16,6}*576
10-fold covers : {80,4}*640a, {16,20}*640a, {160,2}*640, {32,10}*640
11-fold covers : {176,2}*704, {16,22}*704
12-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, {64,6}*768, {192,2}*768, {48,4}*768c, {16,6}*768b, {48,6}*768a
13-fold covers : {208,2}*832, {16,26}*832
14-fold covers : {112,4}*896a, {16,28}*896a, {224,2}*896, {32,14}*896
15-fold covers : {48,10}*960, {80,6}*960, {240,2}*960, {16,30}*960
17-fold covers : {16,34}*1088, {272,2}*1088
18-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, {32,18}*1152, {288,2}*1152, {96,6}*1152a, {96,6}*1152b, {96,6}*1152c, {32,6}*1152
19-fold covers : {16,38}*1216, {304,2}*1216
20-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, {64,10}*1280, {320,2}*1280
21-fold covers : {48,14}*1344, {112,6}*1344, {336,2}*1344, {16,42}*1344
22-fold covers : {16,44}*1408a, {176,4}*1408a, {32,22}*1408, {352,2}*1408
23-fold covers : {16,46}*1472, {368,2}*1472
25-fold covers : {400,2}*1600, {16,50}*1600, {80,10}*1600a, {80,10}*1600b, {80,10}*1600c, {16,10}*1600
26-fold covers : {16,52}*1664a, {208,4}*1664a, {32,26}*1664, {416,2}*1664
27-fold covers : {432,2}*1728, {16,54}*1728, {144,6}*1728a, {144,6}*1728b, {48,18}*1728a, {48,6}*1728a, {48,6}*1728b, {48,18}*1728b, {48,6}*1728c, {16,6}*1728a, {48,6}*1728d, {48,6}*1728e, {48,6}*1728f, {16,6}*1728b, {48,6}*1728g, {48,6}*1728h
28-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, {64,14}*1792, {448,2}*1792
29-fold covers : {16,58}*1856, {464,2}*1856
30-fold covers : {16,60}*1920a, {240,4}*1920a, {80,12}*1920a, {48,20}*1920a, {32,30}*1920, {480,2}*1920, {96,10}*1920, {160,6}*1920
31-fold covers : {16,62}*1984, {496,2}*1984
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := (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*s2*s0*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(18)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(18)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(18)!(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*s2*s0*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 >;
to this polytope