Polytope of Type {16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16}*32
Also Known As : 16-gon, {16}. if this polytope has another name.
Group : SmallGroup(32,18)
Rank : 2
Schlafli Type : {16}
Number of vertices, edges, etc : 16, 16
Order of s0s1 : 16
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{16,2} of size 64
{16,4} of size 128
{16,4} of size 128
{16,6} of size 192
{16,4} of size 256
{16,4} of size 256
{16,8} of size 256
{16,8} of size 256
{16,8} of size 256
{16,8} of size 256
{16,8} of size 256
{16,8} of size 256
{16,10} of size 320
{16,12} of size 384
{16,12} of size 384
{16,14} of size 448
{16,4} of size 512
{16,8} of size 512
{16,8} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,8} of size 512
{16,8} of size 512
{16,8} of size 512
{16,8} of size 512
{16,4} of size 512
{16,4} of size 512
{16,4} of size 512
{16,8} of size 512
{16,8} of size 512
{16,4} of size 512
{16,4} of size 512
{16,18} of size 576
{16,6} of size 576
{16,20} of size 640
{16,20} of size 640
{16,22} of size 704
{16,12} of size 768
{16,12} of size 768
{16,24} of size 768
{16,24} of size 768
{16,24} of size 768
{16,24} of size 768
{16,24} of size 768
{16,24} of size 768
{16,3} of size 768
{16,3} of size 768
{16,6} of size 768
{16,6} of size 768
{16,6} of size 768
{16,26} of size 832
{16,28} of size 896
{16,28} of size 896
{16,30} of size 960
{16,34} of size 1088
{16,36} of size 1152
{16,4} of size 1152
{16,12} of size 1152
{16,36} of size 1152
{16,4} of size 1152
{16,12} of size 1152
{16,38} of size 1216
{16,20} of size 1280
{16,20} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,42} of size 1344
{16,3} of size 1344
{16,3} of size 1344
{16,6} of size 1344
{16,6} of size 1344
{16,7} of size 1344
{16,7} of size 1344
{16,44} of size 1408
{16,44} of size 1408
{16,46} of size 1472
{16,50} of size 1600
{16,10} of size 1600
{16,52} of size 1664
{16,52} of size 1664
{16,54} of size 1728
{16,6} of size 1728
{16,6} of size 1728
{16,28} of size 1792
{16,28} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,58} of size 1856
{16,60} of size 1920
{16,60} of size 1920
{16,10} of size 1920
{16,10} of size 1920
{16,62} of size 1984
Vertex Figure Of :
{2,16} of size 64
{4,16} of size 128
{4,16} of size 128
{6,16} of size 192
{4,16} of size 256
{4,16} of size 256
{8,16} of size 256
{8,16} of size 256
{8,16} of size 256
{8,16} of size 256
{8,16} of size 256
{8,16} of size 256
{10,16} of size 320
{12,16} of size 384
{12,16} of size 384
{14,16} of size 448
{4,16} of size 512
{8,16} of size 512
{8,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{16,16} of size 512
{8,16} of size 512
{8,16} of size 512
{8,16} of size 512
{8,16} of size 512
{4,16} of size 512
{4,16} of size 512
{4,16} of size 512
{8,16} of size 512
{8,16} of size 512
{4,16} of size 512
{4,16} of size 512
{18,16} of size 576
{6,16} of size 576
{20,16} of size 640
{20,16} of size 640
{22,16} of size 704
{12,16} of size 768
{12,16} of size 768
{24,16} of size 768
{24,16} of size 768
{24,16} of size 768
{24,16} of size 768
{24,16} of size 768
{24,16} of size 768
{3,16} of size 768
{3,16} of size 768
{6,16} of size 768
{6,16} of size 768
{6,16} of size 768
{26,16} of size 832
{28,16} of size 896
{28,16} of size 896
{30,16} of size 960
{34,16} of size 1088
{36,16} of size 1152
{4,16} of size 1152
{12,16} of size 1152
{36,16} of size 1152
{4,16} of size 1152
{12,16} of size 1152
{38,16} of size 1216
{20,16} of size 1280
{20,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{42,16} of size 1344
{3,16} of size 1344
{3,16} of size 1344
{6,16} of size 1344
{6,16} of size 1344
{7,16} of size 1344
{7,16} of size 1344
{44,16} of size 1408
{44,16} of size 1408
{46,16} of size 1472
{50,16} of size 1600
{10,16} of size 1600
{52,16} of size 1664
{52,16} of size 1664
{54,16} of size 1728
{6,16} of size 1728
{6,16} of size 1728
{28,16} of size 1792
{28,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{58,16} of size 1856
{60,16} of size 1920
{60,16} of size 1920
{10,16} of size 1920
{10,16} of size 1920
{62,16} of size 1984
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8}*16
4-fold quotients : {4}*8
8-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {32}*64
3-fold covers : {48}*96
4-fold covers : {64}*128
5-fold covers : {80}*160
6-fold covers : {96}*192
7-fold covers : {112}*224
8-fold covers : {128}*256
9-fold covers : {144}*288
10-fold covers : {160}*320
11-fold covers : {176}*352
12-fold covers : {192}*384
13-fold covers : {208}*416
14-fold covers : {224}*448
15-fold covers : {240}*480
16-fold covers : {256}*512
17-fold covers : {272}*544
18-fold covers : {288}*576
19-fold covers : {304}*608
20-fold covers : {320}*640
21-fold covers : {336}*672
22-fold covers : {352}*704
23-fold covers : {368}*736
24-fold covers : {384}*768
25-fold covers : {400}*800
26-fold covers : {416}*832
27-fold covers : {432}*864
28-fold covers : {448}*896
29-fold covers : {464}*928
30-fold covers : {480}*960
31-fold covers : {496}*992
33-fold covers : {528}*1056
34-fold covers : {544}*1088
35-fold covers : {560}*1120
36-fold covers : {576}*1152
37-fold covers : {592}*1184
38-fold covers : {608}*1216
39-fold covers : {624}*1248
40-fold covers : {640}*1280
41-fold covers : {656}*1312
42-fold covers : {672}*1344
43-fold covers : {688}*1376
44-fold covers : {704}*1408
45-fold covers : {720}*1440
46-fold covers : {736}*1472
47-fold covers : {752}*1504
49-fold covers : {784}*1568
50-fold covers : {800}*1600
51-fold covers : {816}*1632
52-fold covers : {832}*1664
53-fold covers : {848}*1696
54-fold covers : {864}*1728
55-fold covers : {880}*1760
56-fold covers : {896}*1792
57-fold covers : {912}*1824
58-fold covers : {928}*1856
59-fold covers : {944}*1888
60-fold covers : {960}*1920
61-fold covers : {976}*1952
62-fold covers : {992}*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);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(16)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(16)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
poly := sub<Sym(16)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*s0*s1 >;
References : None.
to this polytope