Polytope of Type {9,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2}*36
if this polytope has a name.
Group : SmallGroup(36,4)
Rank : 3
Schlafli Type : {9,2}
Number of vertices, edges, etc : 9, 9, 2
Order of s0s1s2 : 18
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{9,2,2} of size 72
{9,2,3} of size 108
{9,2,4} of size 144
{9,2,5} of size 180
{9,2,6} of size 216
{9,2,7} of size 252
{9,2,8} of size 288
{9,2,9} of size 324
{9,2,10} of size 360
{9,2,11} of size 396
{9,2,12} of size 432
{9,2,13} of size 468
{9,2,14} of size 504
{9,2,15} of size 540
{9,2,16} of size 576
{9,2,17} of size 612
{9,2,18} of size 648
{9,2,19} of size 684
{9,2,20} of size 720
{9,2,21} of size 756
{9,2,22} of size 792
{9,2,23} of size 828
{9,2,24} of size 864
{9,2,25} of size 900
{9,2,26} of size 936
{9,2,27} of size 972
{9,2,28} of size 1008
{9,2,29} of size 1044
{9,2,30} of size 1080
{9,2,31} of size 1116
{9,2,32} of size 1152
{9,2,33} of size 1188
{9,2,34} of size 1224
{9,2,35} of size 1260
{9,2,36} of size 1296
{9,2,37} of size 1332
{9,2,38} of size 1368
{9,2,39} of size 1404
{9,2,40} of size 1440
{9,2,41} of size 1476
{9,2,42} of size 1512
{9,2,43} of size 1548
{9,2,44} of size 1584
{9,2,45} of size 1620
{9,2,46} of size 1656
{9,2,47} of size 1692
{9,2,48} of size 1728
{9,2,49} of size 1764
{9,2,50} of size 1800
{9,2,51} of size 1836
{9,2,52} of size 1872
{9,2,53} of size 1908
{9,2,54} of size 1944
{9,2,55} of size 1980
Vertex Figure Of :
{2,9,2} of size 72
{4,9,2} of size 144
{6,9,2} of size 216
{4,9,2} of size 288
{8,9,2} of size 576
{18,9,2} of size 648
{6,9,2} of size 648
{6,9,2} of size 648
{6,9,2} of size 648
{6,9,2} of size 648
{6,9,2} of size 864
{12,9,2} of size 864
{3,9,2} of size 1008
{7,9,2} of size 1008
{7,9,2} of size 1008
{7,9,2} of size 1008
{9,9,2} of size 1008
{9,9,2} of size 1008
{8,9,2} of size 1152
{3,9,2} of size 1296
{4,9,2} of size 1296
{9,9,2} of size 1296
{9,9,2} of size 1296
{12,9,2} of size 1296
{12,9,2} of size 1296
{12,9,2} of size 1728
{24,9,2} of size 1728
{10,9,2} of size 1800
{18,9,2} of size 1944
{6,9,2} of size 1944
{6,9,2} of size 1944
{18,9,2} of size 1944
{6,9,2} of size 1944
{18,9,2} of size 1944
{18,9,2} of size 1944
{18,9,2} of size 1944
{6,9,2} of size 1944
{18,9,2} of size 1944
{18,9,2} of size 1944
{18,9,2} of size 1944
{18,9,2} of size 1944
{6,9,2} of size 1944
{18,9,2} of size 1944
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {18,2}*72
3-fold covers : {27,2}*108, {9,6}*108
4-fold covers : {36,2}*144, {18,4}*144a, {9,4}*144
5-fold covers : {45,2}*180
6-fold covers : {54,2}*216, {18,6}*216a, {18,6}*216b
7-fold covers : {63,2}*252
8-fold covers : {36,4}*288a, {72,2}*288, {18,8}*288, {9,8}*288, {18,4}*288
9-fold covers : {81,2}*324, {9,18}*324, {9,6}*324a, {27,6}*324
10-fold covers : {18,10}*360, {90,2}*360
11-fold covers : {99,2}*396
12-fold covers : {108,2}*432, {54,4}*432a, {27,4}*432, {36,6}*432a, {36,6}*432b, {18,12}*432a, {18,12}*432b, {9,6}*432, {9,12}*432
13-fold covers : {117,2}*468
14-fold covers : {18,14}*504, {126,2}*504
15-fold covers : {135,2}*540, {45,6}*540
16-fold covers : {72,4}*576a, {36,4}*576a, {72,4}*576b, {36,8}*576a, {36,8}*576b, {144,2}*576, {18,16}*576, {9,8}*576, {36,4}*576b, {18,4}*576b, {36,4}*576c, {18,8}*576b, {18,8}*576c
17-fold covers : {153,2}*612
18-fold covers : {162,2}*648, {18,18}*648a, {18,18}*648c, {18,6}*648a, {18,6}*648b, {54,6}*648a, {54,6}*648b, {18,6}*648i
19-fold covers : {171,2}*684
20-fold covers : {36,10}*720, {18,20}*720a, {180,2}*720, {90,4}*720a, {45,4}*720
21-fold covers : {189,2}*756, {63,6}*756
22-fold covers : {18,22}*792, {198,2}*792
23-fold covers : {207,2}*828
24-fold covers : {108,4}*864a, {216,2}*864, {54,8}*864, {27,8}*864, {72,6}*864a, {72,6}*864b, {18,24}*864a, {36,12}*864a, {36,12}*864b, {18,24}*864b, {54,4}*864, {9,12}*864, {9,24}*864, {18,6}*864, {36,6}*864, {18,12}*864a, {18,12}*864b
25-fold covers : {225,2}*900, {9,10}*900, {45,10}*900
26-fold covers : {18,26}*936, {234,2}*936
27-fold covers : {243,2}*972, {9,18}*972a, {27,18}*972, {27,6}*972a, {9,6}*972d, {9,18}*972h, {9,18}*972i, {9,6}*972e, {27,6}*972b, {27,6}*972c, {81,6}*972
28-fold covers : {36,14}*1008, {18,28}*1008a, {252,2}*1008, {126,4}*1008a, {63,4}*1008
29-fold covers : {261,2}*1044
30-fold covers : {54,10}*1080, {270,2}*1080, {18,30}*1080a, {90,6}*1080a, {90,6}*1080b, {18,30}*1080b
31-fold covers : {279,2}*1116
32-fold covers : {36,8}*1152a, {72,4}*1152a, {72,8}*1152a, {72,8}*1152b, {72,8}*1152c, {72,8}*1152d, {36,16}*1152a, {144,4}*1152a, {36,16}*1152b, {144,4}*1152b, {36,4}*1152a, {72,4}*1152b, {36,8}*1152b, {18,32}*1152, {288,2}*1152, {9,8}*1152, {18,8}*1152a, {36,4}*1152d, {36,8}*1152e, {36,8}*1152f, {18,4}*1152a, {18,8}*1152d, {18,8}*1152e, {18,8}*1152f, {36,8}*1152g, {36,8}*1152h, {72,4}*1152c, {72,4}*1152d, {18,8}*1152g, {36,4}*1152e, {72,4}*1152e, {18,4}*1152b, {72,4}*1152f
33-fold covers : {297,2}*1188, {99,6}*1188
34-fold covers : {18,34}*1224, {306,2}*1224
35-fold covers : {315,2}*1260
36-fold covers : {324,2}*1296, {162,4}*1296a, {81,4}*1296, {18,36}*1296a, {36,18}*1296a, {36,18}*1296b, {18,12}*1296a, {36,6}*1296a, {36,6}*1296b, {54,12}*1296a, {108,6}*1296a, {108,6}*1296b, {18,36}*1296c, {18,12}*1296e, {54,12}*1296b, {27,6}*1296, {27,12}*1296, {9,18}*1296a, {9,36}*1296, {9,6}*1296b, {9,12}*1296c, {36,6}*1296l, {18,12}*1296l, {18,4}*1296b, {36,4}*1296, {36,6}*1296m
37-fold covers : {333,2}*1332
38-fold covers : {18,38}*1368, {342,2}*1368
39-fold covers : {351,2}*1404, {117,6}*1404
40-fold covers : {72,10}*1440, {18,40}*1440, {36,20}*1440, {180,4}*1440a, {360,2}*1440, {90,8}*1440, {45,8}*1440, {18,20}*1440, {90,4}*1440
41-fold covers : {369,2}*1476
42-fold covers : {54,14}*1512, {378,2}*1512, {18,42}*1512a, {126,6}*1512a, {126,6}*1512b, {18,42}*1512b
43-fold covers : {387,2}*1548
44-fold covers : {36,22}*1584, {18,44}*1584a, {396,2}*1584, {198,4}*1584a, {99,4}*1584
45-fold covers : {405,2}*1620, {45,18}*1620, {45,6}*1620a, {135,6}*1620
46-fold covers : {18,46}*1656, {414,2}*1656
47-fold covers : {423,2}*1692
48-fold covers : {216,4}*1728a, {108,4}*1728a, {216,4}*1728b, {108,8}*1728a, {108,8}*1728b, {432,2}*1728, {54,16}*1728, {27,8}*1728, {144,6}*1728a, {144,6}*1728b, {18,48}*1728a, {36,24}*1728a, {36,12}*1728a, {36,12}*1728b, {36,24}*1728b, {72,12}*1728a, {72,12}*1728b, {36,24}*1728c, {72,12}*1728c, {72,12}*1728d, {36,24}*1728d, {18,48}*1728b, {108,4}*1728b, {54,4}*1728b, {108,4}*1728c, {54,8}*1728b, {54,8}*1728c, {9,6}*1728, {9,24}*1728, {36,12}*1728c, {36,6}*1728a, {36,6}*1728b, {18,12}*1728a, {18,6}*1728a, {72,6}*1728b, {36,6}*1728c, {72,6}*1728c, {18,12}*1728b, {36,12}*1728d, {36,12}*1728e, {36,12}*1728f, {18,12}*1728c, {36,12}*1728g, {18,24}*1728b, {18,24}*1728c, {18,24}*1728d, {18,24}*1728e, {18,12}*1728d, {36,12}*1728h, {9,12}*1728, {18,6}*1728b
49-fold covers : {441,2}*1764, {9,14}*1764, {63,14}*1764
50-fold covers : {18,50}*1800, {450,2}*1800, {18,10}*1800a, {18,10}*1800b, {90,10}*1800a, {90,10}*1800b, {90,10}*1800c
51-fold covers : {459,2}*1836, {153,6}*1836
52-fold covers : {36,26}*1872, {18,52}*1872a, {468,2}*1872, {234,4}*1872a, {117,4}*1872
53-fold covers : {477,2}*1908
54-fold covers : {486,2}*1944, {18,18}*1944a, {18,18}*1944c, {18,54}*1944a, {54,18}*1944a, {54,18}*1944b, {54,6}*1944a, {54,6}*1944b, {18,6}*1944g, {18,6}*1944h, {18,18}*1944s, {18,18}*1944u, {18,18}*1944x, {18,18}*1944y, {18,6}*1944i, {18,6}*1944j, {54,6}*1944c, {54,6}*1944d, {54,6}*1944e, {54,6}*1944f, {162,6}*1944a, {162,6}*1944b, {18,18}*1944ad, {18,18}*1944af, {18,6}*1944m, {18,6}*1944n, {18,6}*1944o, {54,6}*1944g
55-fold covers : {495,2}*1980
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(11)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(11)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(11)!(10,11);
poly := sub<Sym(11)|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 >;
to this polytope