Polytope of Type {36,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,2}*144
if this polytope has a name.
Group : SmallGroup(144,39)
Rank : 3
Schlafli Type : {36,2}
Number of vertices, edges, etc : 36, 36, 2
Order of s0s1s2 : 36
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 :
{36,2,2} of size 288
{36,2,3} of size 432
{36,2,4} of size 576
{36,2,5} of size 720
{36,2,6} of size 864
{36,2,7} of size 1008
{36,2,8} of size 1152
{36,2,9} of size 1296
{36,2,10} of size 1440
{36,2,11} of size 1584
{36,2,12} of size 1728
{36,2,13} of size 1872
Vertex Figure Of :
{2,36,2} of size 288
{4,36,2} of size 576
{4,36,2} of size 576
{4,36,2} of size 576
{6,36,2} of size 864
{6,36,2} of size 864
{6,36,2} of size 864
{8,36,2} of size 1152
{8,36,2} of size 1152
{4,36,2} of size 1152
{4,36,2} of size 1152
{4,36,2} of size 1152
{6,36,2} of size 1296
{6,36,2} of size 1296
{6,36,2} of size 1296
{10,36,2} of size 1440
{12,36,2} of size 1728
{12,36,2} of size 1728
{6,36,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {18,2}*72
3-fold quotients : {12,2}*48
4-fold quotients : {9,2}*36
6-fold quotients : {6,2}*24
9-fold quotients : {4,2}*16
12-fold quotients : {3,2}*12
18-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {36,4}*288a, {72,2}*288
3-fold covers : {108,2}*432, {36,6}*432a, {36,6}*432b
4-fold covers : {72,4}*576a, {36,4}*576a, {72,4}*576b, {36,8}*576a, {36,8}*576b, {144,2}*576, {36,4}*576b
5-fold covers : {36,10}*720, {180,2}*720
6-fold covers : {108,4}*864a, {216,2}*864, {72,6}*864a, {72,6}*864b, {36,12}*864a, {36,12}*864b
7-fold covers : {36,14}*1008, {252,2}*1008
8-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, {288,2}*1152, {36,4}*1152d, {36,8}*1152e, {36,8}*1152f, {72,4}*1152c, {72,4}*1152d
9-fold covers : {324,2}*1296, {36,18}*1296a, {36,18}*1296b, {36,6}*1296a, {36,6}*1296b, {108,6}*1296a, {108,6}*1296b, {36,6}*1296l, {36,6}*1296m
10-fold covers : {72,10}*1440, {36,20}*1440, {180,4}*1440a, {360,2}*1440
11-fold covers : {36,22}*1584, {396,2}*1584
12-fold covers : {216,4}*1728a, {108,4}*1728a, {216,4}*1728b, {108,8}*1728a, {108,8}*1728b, {432,2}*1728, {144,6}*1728a, {144,6}*1728b, {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, {108,4}*1728b, {36,6}*1728a, {36,6}*1728b, {36,12}*1728e, {36,12}*1728f
13-fold covers : {36,26}*1872, {468,2}*1872
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);;
s2 := (37,38);;
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*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(38)!( 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(38)!( 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);
s2 := Sym(38)!(37,38);
poly := sub<Sym(38)|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*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 >;
to this polytope