Polytope of Type {9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9}*18
Also Known As : nonagon, {9}. if this polytope has another name.
Group : SmallGroup(18,1)
Rank : 2
Schlafli Type : {9}
Number of vertices, edges, etc : 9, 9
Order of s0s1 : 9
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{9,2} of size 36
{9,4} of size 72
{9,6} of size 108
{9,4} of size 144
{9,8} of size 288
{9,18} of size 324
{9,6} of size 324
{9,6} of size 324
{9,6} of size 324
{9,6} of size 324
{9,6} of size 432
{9,12} of size 432
{9,3} of size 504
{9,7} of size 504
{9,7} of size 504
{9,7} of size 504
{9,9} of size 504
{9,9} of size 504
{9,8} of size 576
{9,3} of size 648
{9,4} of size 648
{9,9} of size 648
{9,9} of size 648
{9,12} of size 648
{9,12} of size 648
{9,12} of size 864
{9,24} of size 864
{9,10} of size 900
{9,18} of size 972
{9,6} of size 972
{9,6} of size 972
{9,18} of size 972
{9,6} of size 972
{9,18} of size 972
{9,18} of size 972
{9,18} of size 972
{9,6} of size 972
{9,18} of size 972
{9,18} of size 972
{9,18} of size 972
{9,18} of size 972
{9,6} of size 972
{9,18} of size 972
{9,3} of size 1008
{9,6} of size 1008
{9,6} of size 1008
{9,7} of size 1008
{9,7} of size 1008
{9,7} of size 1008
{9,9} of size 1008
{9,9} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,14} of size 1008
{9,18} of size 1008
{9,18} of size 1008
{9,18} of size 1008
{9,18} of size 1008
{9,10} of size 1080
{9,8} of size 1152
{9,4} of size 1152
{9,9} of size 1152
{9,18} of size 1296
{9,36} of size 1296
{9,6} of size 1296
{9,6} of size 1296
{9,12} of size 1296
{9,6} of size 1296
{9,12} of size 1296
{9,12} of size 1296
{9,6} of size 1296
{9,12} of size 1296
{9,4} of size 1296
{9,6} of size 1296
{9,4} of size 1296
{9,6} of size 1296
{9,12} of size 1296
{9,12} of size 1296
{9,18} of size 1296
{9,18} of size 1296
{9,6} of size 1728
{9,24} of size 1728
{9,12} of size 1728
{9,14} of size 1764
{9,4} of size 1944
{9,9} of size 1944
{9,9} of size 1944
{9,9} of size 1944
{9,9} of size 1944
{9,12} of size 1944
{9,12} of size 1944
{9,12} of size 1944
Vertex Figure Of :
{2,9} of size 36
{4,9} of size 72
{6,9} of size 108
{4,9} of size 144
{8,9} of size 288
{18,9} of size 324
{6,9} of size 324
{6,9} of size 324
{6,9} of size 324
{6,9} of size 324
{6,9} of size 432
{12,9} of size 432
{3,9} of size 504
{7,9} of size 504
{7,9} of size 504
{7,9} of size 504
{9,9} of size 504
{9,9} of size 504
{8,9} of size 576
{3,9} of size 648
{4,9} of size 648
{9,9} of size 648
{9,9} of size 648
{12,9} of size 648
{12,9} of size 648
{12,9} of size 864
{24,9} of size 864
{10,9} of size 900
{18,9} of size 972
{6,9} of size 972
{6,9} of size 972
{18,9} of size 972
{6,9} of size 972
{18,9} of size 972
{18,9} of size 972
{18,9} of size 972
{6,9} of size 972
{18,9} of size 972
{18,9} of size 972
{18,9} of size 972
{18,9} of size 972
{6,9} of size 972
{18,9} of size 972
{3,9} of size 1008
{6,9} of size 1008
{6,9} of size 1008
{7,9} of size 1008
{7,9} of size 1008
{7,9} of size 1008
{9,9} of size 1008
{9,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{14,9} of size 1008
{18,9} of size 1008
{18,9} of size 1008
{18,9} of size 1008
{18,9} of size 1008
{10,9} of size 1080
{8,9} of size 1152
{4,9} of size 1152
{9,9} of size 1152
{18,9} of size 1296
{36,9} of size 1296
{6,9} of size 1296
{6,9} of size 1296
{12,9} of size 1296
{6,9} of size 1296
{12,9} of size 1296
{12,9} of size 1296
{6,9} of size 1296
{12,9} of size 1296
{4,9} of size 1296
{6,9} of size 1296
{4,9} of size 1296
{6,9} of size 1296
{12,9} of size 1296
{12,9} of size 1296
{18,9} of size 1296
{18,9} of size 1296
{6,9} of size 1728
{24,9} of size 1728
{12,9} of size 1728
{14,9} of size 1764
{4,9} of size 1944
{9,9} of size 1944
{9,9} of size 1944
{9,9} of size 1944
{9,9} of size 1944
{12,9} of size 1944
{12,9} of size 1944
{12,9} of size 1944
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3}*6
Covers (Minimal Covers in Boldface) :
2-fold covers : {18}*36
3-fold covers : {27}*54
4-fold covers : {36}*72
5-fold covers : {45}*90
6-fold covers : {54}*108
7-fold covers : {63}*126
8-fold covers : {72}*144
9-fold covers : {81}*162
10-fold covers : {90}*180
11-fold covers : {99}*198
12-fold covers : {108}*216
13-fold covers : {117}*234
14-fold covers : {126}*252
15-fold covers : {135}*270
16-fold covers : {144}*288
17-fold covers : {153}*306
18-fold covers : {162}*324
19-fold covers : {171}*342
20-fold covers : {180}*360
21-fold covers : {189}*378
22-fold covers : {198}*396
23-fold covers : {207}*414
24-fold covers : {216}*432
25-fold covers : {225}*450
26-fold covers : {234}*468
27-fold covers : {243}*486
28-fold covers : {252}*504
29-fold covers : {261}*522
30-fold covers : {270}*540
31-fold covers : {279}*558
32-fold covers : {288}*576
33-fold covers : {297}*594
34-fold covers : {306}*612
35-fold covers : {315}*630
36-fold covers : {324}*648
37-fold covers : {333}*666
38-fold covers : {342}*684
39-fold covers : {351}*702
40-fold covers : {360}*720
41-fold covers : {369}*738
42-fold covers : {378}*756
43-fold covers : {387}*774
44-fold covers : {396}*792
45-fold covers : {405}*810
46-fold covers : {414}*828
47-fold covers : {423}*846
48-fold covers : {432}*864
49-fold covers : {441}*882
50-fold covers : {450}*900
51-fold covers : {459}*918
52-fold covers : {468}*936
53-fold covers : {477}*954
54-fold covers : {486}*972
55-fold covers : {495}*990
56-fold covers : {504}*1008
57-fold covers : {513}*1026
58-fold covers : {522}*1044
59-fold covers : {531}*1062
60-fold covers : {540}*1080
61-fold covers : {549}*1098
62-fold covers : {558}*1116
63-fold covers : {567}*1134
64-fold covers : {576}*1152
65-fold covers : {585}*1170
66-fold covers : {594}*1188
67-fold covers : {603}*1206
68-fold covers : {612}*1224
69-fold covers : {621}*1242
70-fold covers : {630}*1260
71-fold covers : {639}*1278
72-fold covers : {648}*1296
73-fold covers : {657}*1314
74-fold covers : {666}*1332
75-fold covers : {675}*1350
76-fold covers : {684}*1368
77-fold covers : {693}*1386
78-fold covers : {702}*1404
79-fold covers : {711}*1422
80-fold covers : {720}*1440
81-fold covers : {729}*1458
82-fold covers : {738}*1476
83-fold covers : {747}*1494
84-fold covers : {756}*1512
85-fold covers : {765}*1530
86-fold covers : {774}*1548
87-fold covers : {783}*1566
88-fold covers : {792}*1584
89-fold covers : {801}*1602
90-fold covers : {810}*1620
91-fold covers : {819}*1638
92-fold covers : {828}*1656
93-fold covers : {837}*1674
94-fold covers : {846}*1692
95-fold covers : {855}*1710
96-fold covers : {864}*1728
97-fold covers : {873}*1746
98-fold covers : {882}*1764
99-fold covers : {891}*1782
100-fold covers : {900}*1800
101-fold covers : {909}*1818
102-fold covers : {918}*1836
103-fold covers : {927}*1854
104-fold covers : {936}*1872
105-fold covers : {945}*1890
106-fold covers : {954}*1908
107-fold covers : {963}*1926
108-fold covers : {972}*1944
109-fold covers : {981}*1962
110-fold covers : {990}*1980
111-fold covers : {999}*1998
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(9)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(9)!(1,2)(3,4)(5,6)(7,8);
poly := sub<Sym(9)|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 >;
References : None.
to this polytope