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# Polytope of Type {2,23}

Atlas Canonical Name : {2,23}*92
if this polytope has a name.
Group : SmallGroup(92,3)
Rank : 3
Schlafli Type : {2,23}
Number of vertices, edges, etc : 2, 23, 23
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 :
{2,23,2} of size 184
Vertex Figure Of :
{2,2,23} of size 184
{3,2,23} of size 276
{4,2,23} of size 368
{5,2,23} of size 460
{6,2,23} of size 552
{7,2,23} of size 644
{8,2,23} of size 736
{9,2,23} of size 828
{10,2,23} of size 920
{11,2,23} of size 1012
{12,2,23} of size 1104
{13,2,23} of size 1196
{14,2,23} of size 1288
{15,2,23} of size 1380
{16,2,23} of size 1472
{17,2,23} of size 1564
{18,2,23} of size 1656
{19,2,23} of size 1748
{20,2,23} of size 1840
{21,2,23} of size 1932
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,46}*184
3-fold covers : {2,69}*276
4-fold covers : {2,92}*368, {4,46}*368
5-fold covers : {2,115}*460
6-fold covers : {6,46}*552, {2,138}*552
7-fold covers : {2,161}*644
8-fold covers : {4,92}*736, {2,184}*736, {8,46}*736
9-fold covers : {2,207}*828, {6,69}*828
10-fold covers : {10,46}*920, {2,230}*920
11-fold covers : {2,253}*1012
12-fold covers : {12,46}*1104, {6,92}*1104a, {2,276}*1104, {4,138}*1104a, {6,69}*1104, {4,69}*1104
13-fold covers : {2,299}*1196
14-fold covers : {14,46}*1288, {2,322}*1288
15-fold covers : {2,345}*1380
16-fold covers : {8,92}*1472a, {4,184}*1472a, {8,92}*1472b, {4,184}*1472b, {4,92}*1472, {16,46}*1472, {2,368}*1472
17-fold covers : {2,391}*1564
18-fold covers : {18,46}*1656, {2,414}*1656, {6,138}*1656a, {6,138}*1656b, {6,138}*1656c
19-fold covers : {2,437}*1748
20-fold covers : {20,46}*1840, {10,92}*1840, {2,460}*1840, {4,230}*1840
21-fold covers : {2,483}*1932
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24);;
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 ];;
poly := F / rels;;

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

```

to this polytope