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# Polytope of Type {4,6}

Atlas Canonical Name : {4,6}*432a
if this polytope has a name.
Group : SmallGroup(432,530)
Rank : 3
Schlafli Type : {4,6}
Number of vertices, edges, etc : 36, 108, 54
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Halving Operation
Facet Of :
{4,6,2} of size 864
{4,6,4} of size 1728
Vertex Figure Of :
{2,4,6} of size 864
{4,4,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6}*216
3-fold quotients : {4,6}*144
6-fold quotients : {4,6}*72
27-fold quotients : {4,2}*16
54-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,6}*864a, {4,12}*864b
3-fold covers : {4,6}*1296a, {12,6}*1296l, {12,6}*1296o
4-fold covers : {16,6}*1728a, {4,12}*1728a, {8,12}*1728a, {4,24}*1728a, {4,24}*1728c, {8,12}*1728d
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)
(17,27)(18,26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)(42,50)
(43,52)(44,54)(45,53);;
s1 := ( 2, 3)( 4,10)( 5,12)( 6,11)( 7,19)( 8,21)( 9,20)(13,14)(16,24)(17,23)
(18,22)(25,26)(29,30)(31,37)(32,39)(33,38)(34,46)(35,48)(36,47)(40,41)(43,51)
(44,50)(45,49)(52,53);;
s2 := ( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,49)
(11,50)(12,51)(13,46)(14,47)(15,48)(16,52)(17,53)(18,54)(19,40)(20,41)(21,42)
(22,37)(23,38)(24,39)(25,43)(26,44)(27,45);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(54)!( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)
(16,25)(17,27)(18,26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)
(42,50)(43,52)(44,54)(45,53);
s1 := Sym(54)!( 2, 3)( 4,10)( 5,12)( 6,11)( 7,19)( 8,21)( 9,20)(13,14)(16,24)
(17,23)(18,22)(25,26)(29,30)(31,37)(32,39)(33,38)(34,46)(35,48)(36,47)(40,41)
(43,51)(44,50)(45,49)(52,53);
s2 := Sym(54)!( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)
(10,49)(11,50)(12,51)(13,46)(14,47)(15,48)(16,52)(17,53)(18,54)(19,40)(20,41)
(21,42)(22,37)(23,38)(24,39)(25,43)(26,44)(27,45);
poly := sub<Sym(54)|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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 >;

```
References : None.
to this polytope