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# Polytope of Type {23,2}

Atlas Canonical Name : {23,2}*92
if this polytope has a name.
Group : SmallGroup(92,3)
Rank : 3
Schlafli Type : {23,2}
Number of vertices, edges, etc : 23, 23, 2
Order of s0s1s2 : 46
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{23,2,2} of size 184
{23,2,3} of size 276
{23,2,4} of size 368
{23,2,5} of size 460
{23,2,6} of size 552
{23,2,7} of size 644
{23,2,8} of size 736
{23,2,9} of size 828
{23,2,10} of size 920
{23,2,11} of size 1012
{23,2,12} of size 1104
{23,2,13} of size 1196
{23,2,14} of size 1288
{23,2,15} of size 1380
{23,2,16} of size 1472
{23,2,17} of size 1564
{23,2,18} of size 1656
{23,2,19} of size 1748
{23,2,20} of size 1840
{23,2,21} of size 1932
Vertex Figure Of :
{2,23,2} of size 184
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {46,2}*184
3-fold covers : {69,2}*276
4-fold covers : {92,2}*368, {46,4}*368
5-fold covers : {115,2}*460
6-fold covers : {46,6}*552, {138,2}*552
7-fold covers : {161,2}*644
8-fold covers : {92,4}*736, {184,2}*736, {46,8}*736
9-fold covers : {207,2}*828, {69,6}*828
10-fold covers : {46,10}*920, {230,2}*920
11-fold covers : {253,2}*1012
12-fold covers : {46,12}*1104, {92,6}*1104a, {276,2}*1104, {138,4}*1104a, {69,6}*1104, {69,4}*1104
13-fold covers : {299,2}*1196
14-fold covers : {46,14}*1288, {322,2}*1288
15-fold covers : {345,2}*1380
16-fold covers : {92,8}*1472a, {184,4}*1472a, {92,8}*1472b, {184,4}*1472b, {92,4}*1472, {46,16}*1472, {368,2}*1472
17-fold covers : {391,2}*1564
18-fold covers : {46,18}*1656, {414,2}*1656, {138,6}*1656a, {138,6}*1656b, {138,6}*1656c
19-fold covers : {437,2}*1748
20-fold covers : {46,20}*1840, {92,10}*1840, {460,2}*1840, {230,4}*1840
21-fold covers : {483,2}*1932
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);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22);;
s2 := (24,25);;
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 ];;
poly := F / rels;;

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

```

to this polytope