# Polytope of Type {4,3,6,3}

Atlas Canonical Name : {4,3,6,3}*432
if this polytope has a name.
Group : SmallGroup(432,523)
Rank : 5
Schlafli Type : {4,3,6,3}
Number of vertices, edges, etc : 4, 6, 9, 9, 3
Order of s0s1s2s3s4 : 3
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,6,3,2} of size 864
{4,3,6,3,4} of size 1728
Vertex Figure Of :
{2,4,3,6,3} of size 864
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,3,2,3}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,6,3}*864, {4,3,6,6}*864a, {4,6,6,3}*864b, {4,6,6,3}*864c
3-fold covers : {4,3,6,9}*1296, {4,3,6,3}*1296a, {4,9,6,3}*1296, {4,3,6,3}*1296b
4-fold covers : {4,12,6,3}*1728b, {4,12,6,3}*1728c, {4,3,6,12}*1728a, {8,3,6,3}*1728, {4,3,6,6}*1728a, {4,6,6,3}*1728a, {4,6,6,6}*1728b, {4,6,6,6}*1728c
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)
(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(26,27)(29,33)(30,35)(31,34)(32,36);;
s2 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,21)(14,24)(15,23)(16,22)(18,20)
(25,29)(26,32)(27,31)(28,30)(34,36);;
s3 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,21)( 6,22)( 7,23)( 8,24)( 9,17)(10,18)
(11,19)(12,20)(29,33)(30,34)(31,35)(32,36);;
s4 := ( 5, 9)( 6,10)( 7,11)( 8,12)(13,25)(14,26)(15,27)(16,28)(17,33)(18,34)
(19,35)(20,36)(21,29)(22,30)(23,31)(24,32);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(36)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)
(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36);
s1 := Sym(36)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)
(20,24)(26,27)(29,33)(30,35)(31,34)(32,36);
s2 := Sym(36)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,21)(14,24)(15,23)(16,22)
(18,20)(25,29)(26,32)(27,31)(28,30)(34,36);
s3 := Sym(36)!( 1,13)( 2,14)( 3,15)( 4,16)( 5,21)( 6,22)( 7,23)( 8,24)( 9,17)
(10,18)(11,19)(12,20)(29,33)(30,34)(31,35)(32,36);
s4 := Sym(36)!( 5, 9)( 6,10)( 7,11)( 8,12)(13,25)(14,26)(15,27)(16,28)(17,33)
(18,34)(19,35)(20,36)(21,29)(22,30)(23,31)(24,32);
poly := sub<Sym(36)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 >;

```
References : None.
to this polytope