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# Polytope of Type {33,2}

Atlas Canonical Name : {33,2}*132
if this polytope has a name.
Group : SmallGroup(132,9)
Rank : 3
Schlafli Type : {33,2}
Number of vertices, edges, etc : 33, 33, 2
Order of s0s1s2 : 66
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{33,2,2} of size 264
{33,2,3} of size 396
{33,2,4} of size 528
{33,2,5} of size 660
{33,2,6} of size 792
{33,2,7} of size 924
{33,2,8} of size 1056
{33,2,9} of size 1188
{33,2,10} of size 1320
{33,2,11} of size 1452
{33,2,12} of size 1584
{33,2,13} of size 1716
{33,2,14} of size 1848
{33,2,15} of size 1980
Vertex Figure Of :
{2,33,2} of size 264
{4,33,2} of size 528
{6,33,2} of size 792
{6,33,2} of size 1056
{4,33,2} of size 1056
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {11,2}*44
11-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {66,2}*264
3-fold covers : {99,2}*396, {33,6}*396
4-fold covers : {132,2}*528, {66,4}*528a, {33,4}*528
5-fold covers : {165,2}*660
6-fold covers : {198,2}*792, {66,6}*792b, {66,6}*792c
7-fold covers : {231,2}*924
8-fold covers : {132,4}*1056a, {264,2}*1056, {66,8}*1056, {33,8}*1056, {66,4}*1056
9-fold covers : {297,2}*1188, {99,6}*1188, {33,6}*1188
10-fold covers : {66,10}*1320, {330,2}*1320
11-fold covers : {363,2}*1452, {33,22}*1452
12-fold covers : {396,2}*1584, {198,4}*1584a, {99,4}*1584, {66,12}*1584b, {132,6}*1584b, {132,6}*1584c, {66,12}*1584c, {33,12}*1584, {33,6}*1584
13-fold covers : {429,2}*1716
14-fold covers : {66,14}*1848, {462,2}*1848
15-fold covers : {495,2}*1980, {165,6}*1980
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27)(28,29)(30,31)(32,33);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);;
s2 := (34,35);;
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 ];;
poly := F / rels;;

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

```

to this polytope