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# Polytope of Type {10,5}

Atlas Canonical Name : {10,5}*100
if this polytope has a name.
Group : SmallGroup(100,13)
Rank : 3
Schlafli Type : {10,5}
Number of vertices, edges, etc : 10, 25, 5
Order of s0s1s2 : 10
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{10,5,2} of size 200
{10,5,10} of size 1000
{10,5,4} of size 1600
Vertex Figure Of :
{2,10,5} of size 200
{4,10,5} of size 400
{5,10,5} of size 500
{6,10,5} of size 600
{8,10,5} of size 800
{10,10,5} of size 1000
{10,10,5} of size 1000
{12,10,5} of size 1200
{14,10,5} of size 1400
{15,10,5} of size 1500
{3,10,5} of size 1500
{16,10,5} of size 1600
{18,10,5} of size 1800
{20,10,5} of size 2000
{20,10,5} of size 2000
{4,10,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,10}*200b
3-fold covers : {10,15}*300
4-fold covers : {10,20}*400b, {20,10}*400c
5-fold covers : {10,25}*500, {10,5}*500
6-fold covers : {30,10}*600a, {10,30}*600c
7-fold covers : {10,35}*700
8-fold covers : {10,40}*800b, {20,20}*800b, {40,10}*800c
9-fold covers : {10,45}*900, {30,15}*900
10-fold covers : {10,50}*1000b, {10,10}*1000b, {10,10}*1000d
11-fold covers : {10,55}*1100
12-fold covers : {30,20}*1200a, {60,10}*1200a, {10,60}*1200c, {20,30}*1200c, {20,15}*1200, {30,15}*1200
13-fold covers : {10,65}*1300
14-fold covers : {70,10}*1400a, {10,70}*1400c
15-fold covers : {10,75}*1500, {10,15}*1500e
16-fold covers : {10,80}*1600b, {40,20}*1600a, {20,20}*1600b, {40,20}*1600b, {20,40}*1600d, {20,40}*1600f, {80,10}*1600c, {10,5}*1600, {20,5}*1600
17-fold covers : {10,85}*1700
18-fold covers : {90,10}*1800a, {10,90}*1800c, {30,30}*1800b, {30,30}*1800d, {30,30}*1800h
19-fold covers : {10,95}*1900
20-fold covers : {10,100}*2000b, {10,20}*2000a, {20,50}*2000b, {20,10}*2000c, {10,20}*2000h, {20,10}*2000h
Permutation Representation (GAP) :
```s0 := ( 4, 5)( 7, 8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);;
s1 := ( 1, 4)( 2,10)( 3, 7)( 5,12)( 6,18)( 8,20)( 9,14)(11,16)(15,24)(17,21)
(19,22)(23,25);;
s2 := ( 1, 2)( 3, 6)( 4, 8)( 5, 7)(10,15)(11,14)(12,17)(13,16)(18,19)(20,23)
(21,22)(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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope