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# Polytope of Type {29,2}

Atlas Canonical Name : {29,2}*116
if this polytope has a name.
Group : SmallGroup(116,4)
Rank : 3
Schlafli Type : {29,2}
Number of vertices, edges, etc : 29, 29, 2
Order of s0s1s2 : 58
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{29,2,2} of size 232
{29,2,3} of size 348
{29,2,4} of size 464
{29,2,5} of size 580
{29,2,6} of size 696
{29,2,7} of size 812
{29,2,8} of size 928
{29,2,9} of size 1044
{29,2,10} of size 1160
{29,2,11} of size 1276
{29,2,12} of size 1392
{29,2,13} of size 1508
{29,2,14} of size 1624
{29,2,15} of size 1740
{29,2,16} of size 1856
{29,2,17} of size 1972
Vertex Figure Of :
{2,29,2} of size 232
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {58,2}*232
3-fold covers : {87,2}*348
4-fold covers : {116,2}*464, {58,4}*464
5-fold covers : {145,2}*580
6-fold covers : {58,6}*696, {174,2}*696
7-fold covers : {203,2}*812
8-fold covers : {116,4}*928, {232,2}*928, {58,8}*928
9-fold covers : {261,2}*1044, {87,6}*1044
10-fold covers : {58,10}*1160, {290,2}*1160
11-fold covers : {319,2}*1276
12-fold covers : {58,12}*1392, {116,6}*1392a, {348,2}*1392, {174,4}*1392a, {87,6}*1392, {87,4}*1392
13-fold covers : {377,2}*1508
14-fold covers : {58,14}*1624, {406,2}*1624
15-fold covers : {435,2}*1740
16-fold covers : {116,8}*1856a, {232,4}*1856a, {116,8}*1856b, {232,4}*1856b, {116,4}*1856, {58,16}*1856, {464,2}*1856
17-fold covers : {493,2}*1972
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);;
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);;
s2 := (30,31);;
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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(31)!( 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);
s1 := Sym(31)!( 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);
s2 := Sym(31)!(30,31);
poly := sub<Sym(31)|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 >;

```

to this polytope