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# Polytope of Type {5,10}

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

```
References : None.
to this polytope