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# Polytope of Type {2,36}

Atlas Canonical Name : {2,36}*144
if this polytope has a name.
Group : SmallGroup(144,39)
Rank : 3
Schlafli Type : {2,36}
Number of vertices, edges, etc : 2, 36, 36
Order of s0s1s2 : 36
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,36,2} of size 288
{2,36,4} of size 576
{2,36,4} of size 576
{2,36,4} of size 576
{2,36,6} of size 864
{2,36,6} of size 864
{2,36,6} of size 864
{2,36,8} of size 1152
{2,36,8} of size 1152
{2,36,4} of size 1152
{2,36,4} of size 1152
{2,36,4} of size 1152
{2,36,6} of size 1296
{2,36,6} of size 1296
{2,36,6} of size 1296
{2,36,10} of size 1440
{2,36,12} of size 1728
{2,36,12} of size 1728
{2,36,6} of size 1728
Vertex Figure Of :
{2,2,36} of size 288
{3,2,36} of size 432
{4,2,36} of size 576
{5,2,36} of size 720
{6,2,36} of size 864
{7,2,36} of size 1008
{8,2,36} of size 1152
{9,2,36} of size 1296
{10,2,36} of size 1440
{11,2,36} of size 1584
{12,2,36} of size 1728
{13,2,36} of size 1872
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,18}*72
3-fold quotients : {2,12}*48
4-fold quotients : {2,9}*36
6-fold quotients : {2,6}*24
9-fold quotients : {2,4}*16
12-fold quotients : {2,3}*12
18-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,36}*288a, {2,72}*288
3-fold covers : {2,108}*432, {6,36}*432a, {6,36}*432b
4-fold covers : {4,72}*576a, {4,36}*576a, {4,72}*576b, {8,36}*576a, {8,36}*576b, {2,144}*576, {4,36}*576b
5-fold covers : {10,36}*720, {2,180}*720
6-fold covers : {4,108}*864a, {2,216}*864, {6,72}*864a, {6,72}*864b, {12,36}*864a, {12,36}*864b
7-fold covers : {14,36}*1008, {2,252}*1008
8-fold covers : {8,36}*1152a, {4,72}*1152a, {8,72}*1152a, {8,72}*1152b, {8,72}*1152c, {8,72}*1152d, {16,36}*1152a, {4,144}*1152a, {16,36}*1152b, {4,144}*1152b, {4,36}*1152a, {4,72}*1152b, {8,36}*1152b, {2,288}*1152, {4,36}*1152d, {8,36}*1152e, {8,36}*1152f, {4,72}*1152c, {4,72}*1152d
9-fold covers : {2,324}*1296, {18,36}*1296a, {18,36}*1296b, {6,36}*1296a, {6,36}*1296b, {6,108}*1296a, {6,108}*1296b, {6,36}*1296l, {6,36}*1296m
10-fold covers : {10,72}*1440, {20,36}*1440, {4,180}*1440a, {2,360}*1440
11-fold covers : {22,36}*1584, {2,396}*1584
12-fold covers : {4,216}*1728a, {4,108}*1728a, {4,216}*1728b, {8,108}*1728a, {8,108}*1728b, {2,432}*1728, {6,144}*1728a, {6,144}*1728b, {24,36}*1728a, {12,36}*1728a, {12,36}*1728b, {24,36}*1728b, {12,72}*1728a, {12,72}*1728b, {24,36}*1728c, {12,72}*1728c, {12,72}*1728d, {24,36}*1728d, {4,108}*1728b, {6,36}*1728a, {6,36}*1728b, {12,36}*1728e, {12,36}*1728f
13-fold covers : {26,36}*1872, {2,468}*1872
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)
(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)(18,21)
(20,31)(22,33)(24,27)(26,29)(28,37)(30,34)(32,35)(36,38);;
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*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)
(23,24)(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38);
s2 := Sym(38)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)
(18,21)(20,31)(22,33)(24,27)(26,29)(28,37)(30,34)(32,35)(36,38);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope