Polytope of Type {36}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36}*72
Also Known As : 36-gon, {36}. if this polytope has another name.
Group : SmallGroup(72,6)
Rank : 2
Schlafli Type : {36}
Number of vertices, edges, etc : 36, 36
Order of s0s1 : 36
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{36,2} of size 144
{36,4} of size 288
{36,4} of size 288
{36,4} of size 288
{36,6} of size 432
{36,6} of size 432
{36,6} of size 432
{36,4} of size 576
{36,8} of size 576
{36,8} of size 576
{36,4} of size 576
{36,4} of size 576
{36,6} of size 648
{36,6} of size 648
{36,6} of size 648
{36,10} of size 720
{36,12} of size 864
{36,12} of size 864
{36,6} of size 864
{36,14} of size 1008
{36,8} of size 1152
{36,16} of size 1152
{36,16} of size 1152
{36,4} of size 1152
{36,8} of size 1152
{36,4} of size 1152
{36,4} of size 1152
{36,8} of size 1152
{36,8} of size 1152
{36,4} of size 1152
{36,8} of size 1152
{36,8} of size 1152
{36,8} of size 1152
{36,8} of size 1152
{36,4} of size 1152
{36,18} of size 1296
{36,18} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,18} of size 1296
{36,6} of size 1296
{36,9} of size 1296
{36,18} of size 1296
{36,6} of size 1296
{36,3} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,4} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,6} of size 1296
{36,20} of size 1440
{36,22} of size 1584
{36,24} of size 1728
{36,12} of size 1728
{36,12} of size 1728
{36,24} of size 1728
{36,24} of size 1728
{36,24} of size 1728
{36,12} of size 1728
{36,6} of size 1728
{36,6} of size 1728
{36,6} of size 1728
{36,12} of size 1728
{36,12} of size 1728
{36,12} of size 1728
{36,12} of size 1728
{36,12} of size 1728
{36,12} of size 1728
{36,10} of size 1800
{36,26} of size 1872
{36,6} of size 1944
Vertex Figure Of :
{2,36} of size 144
{4,36} of size 288
{4,36} of size 288
{4,36} of size 288
{6,36} of size 432
{6,36} of size 432
{6,36} of size 432
{4,36} of size 576
{8,36} of size 576
{8,36} of size 576
{4,36} of size 576
{4,36} of size 576
{6,36} of size 648
{6,36} of size 648
{6,36} of size 648
{10,36} of size 720
{12,36} of size 864
{12,36} of size 864
{6,36} of size 864
{14,36} of size 1008
{8,36} of size 1152
{16,36} of size 1152
{16,36} of size 1152
{4,36} of size 1152
{8,36} of size 1152
{4,36} of size 1152
{4,36} of size 1152
{8,36} of size 1152
{8,36} of size 1152
{4,36} of size 1152
{8,36} of size 1152
{8,36} of size 1152
{8,36} of size 1152
{8,36} of size 1152
{4,36} of size 1152
{18,36} of size 1296
{18,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{18,36} of size 1296
{6,36} of size 1296
{9,36} of size 1296
{18,36} of size 1296
{6,36} of size 1296
{3,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{4,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{6,36} of size 1296
{20,36} of size 1440
{22,36} of size 1584
{24,36} of size 1728
{12,36} of size 1728
{12,36} of size 1728
{24,36} of size 1728
{24,36} of size 1728
{24,36} of size 1728
{12,36} of size 1728
{6,36} of size 1728
{6,36} of size 1728
{6,36} of size 1728
{12,36} of size 1728
{12,36} of size 1728
{12,36} of size 1728
{12,36} of size 1728
{12,36} of size 1728
{12,36} of size 1728
{10,36} of size 1800
{26,36} of size 1872
{6,36} of size 1944
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {18}*36
3-fold quotients : {12}*24
4-fold quotients : {9}*18
6-fold quotients : {6}*12
9-fold quotients : {4}*8
12-fold quotients : {3}*6
18-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {72}*144
3-fold covers : {108}*216
4-fold covers : {144}*288
5-fold covers : {180}*360
6-fold covers : {216}*432
7-fold covers : {252}*504
8-fold covers : {288}*576
9-fold covers : {324}*648
10-fold covers : {360}*720
11-fold covers : {396}*792
12-fold covers : {432}*864
13-fold covers : {468}*936
14-fold covers : {504}*1008
15-fold covers : {540}*1080
16-fold covers : {576}*1152
17-fold covers : {612}*1224
18-fold covers : {648}*1296
19-fold covers : {684}*1368
20-fold covers : {720}*1440
21-fold covers : {756}*1512
22-fold covers : {792}*1584
23-fold covers : {828}*1656
24-fold covers : {864}*1728
25-fold covers : {900}*1800
26-fold covers : {936}*1872
27-fold covers : {972}*1944
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22)
(23,26)(24,25)(27,28)(29,30)(31,34)(32,33)(35,36);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)(16,19)
(18,29)(20,31)(22,25)(24,27)(26,35)(28,32)(30,33)(34,36);;
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*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(36)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)
(21,22)(23,26)(24,25)(27,28)(29,30)(31,34)(32,33)(35,36);
s1 := Sym(36)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)
(16,19)(18,29)(20,31)(22,25)(24,27)(26,35)(28,32)(30,33)(34,36);
poly := sub<Sym(36)|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*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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope