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# Polytope of Type {50,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,2}*200
if this polytope has a name.
Group : SmallGroup(200,13)
Rank : 3
Schlafli Type : {50,2}
Number of vertices, edges, etc : 50, 50, 2
Order of s0s1s2 : 50
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{50,2,2} of size 400
{50,2,3} of size 600
{50,2,4} of size 800
{50,2,5} of size 1000
{50,2,6} of size 1200
{50,2,7} of size 1400
{50,2,8} of size 1600
{50,2,9} of size 1800
{50,2,10} of size 2000
Vertex Figure Of :
{2,50,2} of size 400
{4,50,2} of size 800
{6,50,2} of size 1200
{8,50,2} of size 1600
{10,50,2} of size 2000
{10,50,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {25,2}*100
5-fold quotients : {10,2}*40
10-fold quotients : {5,2}*20
25-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {100,2}*400, {50,4}*400
3-fold covers : {50,6}*600, {150,2}*600
4-fold covers : {100,4}*800, {200,2}*800, {50,8}*800
5-fold covers : {250,2}*1000, {50,10}*1000a, {50,10}*1000b
6-fold covers : {50,12}*1200, {100,6}*1200a, {300,2}*1200, {150,4}*1200a
7-fold covers : {50,14}*1400, {350,2}*1400
8-fold covers : {200,4}*1600a, {100,4}*1600, {200,4}*1600b, {100,8}*1600a, {100,8}*1600b, {400,2}*1600, {50,16}*1600
9-fold covers : {50,18}*1800, {450,2}*1800, {150,6}*1800a, {150,6}*1800b, {150,6}*1800c
10-fold covers : {500,2}*2000, {250,4}*2000, {50,20}*2000a, {100,10}*2000a, {100,10}*2000b, {50,20}*2000b
Permutation Representation (GAP) :
```s0 := ( 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)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)
(45,46)(47,48)(49,50);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)
(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)(40,45)
(42,43)(44,49)(46,47)(48,50);;
s2 := (51,52);;
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*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(52)!( 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)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44)(45,46)(47,48)(49,50);
s1 := Sym(52)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)
(40,45)(42,43)(44,49)(46,47)(48,50);
s2 := Sym(52)!(51,52);
poly := sub<Sym(52)|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*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