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# Polytope of Type {6,24}

Atlas Canonical Name : {6,24}*288b
if this polytope has a name.
Group : SmallGroup(288,441)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 6, 72, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,24,2} of size 576
{6,24,4} of size 1152
{6,24,4} of size 1152
{6,24,4} of size 1152
{6,24,4} of size 1152
{6,24,6} of size 1728
{6,24,6} of size 1728
Vertex Figure Of :
{2,6,24} of size 576
{3,6,24} of size 864
{4,6,24} of size 1152
{6,6,24} of size 1728
{6,6,24} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,12}*144b
3-fold quotients : {2,24}*96
4-fold quotients : {6,6}*72b
6-fold quotients : {2,12}*48
8-fold quotients : {6,3}*36
9-fold quotients : {2,8}*32
12-fold quotients : {2,6}*24
18-fold quotients : {2,4}*16
24-fold quotients : {2,3}*12
36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,48}*576b, {12,24}*576d
3-fold covers : {6,72}*864b, {6,24}*864a, {6,24}*864f
4-fold covers : {12,24}*1152a, {24,24}*1152a, {24,24}*1152h, {12,48}*1152a, {12,48}*1152d, {6,96}*1152b, {12,24}*1152p, {6,24}*1152g
5-fold covers : {30,24}*1440a, {6,120}*1440c
6-fold covers : {6,144}*1728b, {6,48}*1728a, {12,72}*1728b, {12,24}*1728c, {6,48}*1728f, {12,24}*1728o
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)
(65,66)(68,69)(71,72);;
s1 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,29)(20,28)
(21,30)(22,35)(23,34)(24,36)(25,32)(26,31)(27,33)(37,56)(38,55)(39,57)(40,62)
(41,61)(42,63)(43,59)(44,58)(45,60)(46,65)(47,64)(48,66)(49,71)(50,70)(51,72)
(52,68)(53,67)(54,69);;
s2 := ( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)(10,49)
(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,67)(20,69)(21,68)
(22,64)(23,66)(24,65)(25,70)(26,72)(27,71)(28,58)(29,60)(30,59)(31,55)(32,57)
(33,56)(34,61)(35,63)(36,62);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(72)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)
(62,63)(65,66)(68,69)(71,72);
s1 := Sym(72)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,29)
(20,28)(21,30)(22,35)(23,34)(24,36)(25,32)(26,31)(27,33)(37,56)(38,55)(39,57)
(40,62)(41,61)(42,63)(43,59)(44,58)(45,60)(46,65)(47,64)(48,66)(49,71)(50,70)
(51,72)(52,68)(53,67)(54,69);
s2 := Sym(72)!( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)
(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,67)(20,69)
(21,68)(22,64)(23,66)(24,65)(25,70)(26,72)(27,71)(28,58)(29,60)(30,59)(31,55)
(32,57)(33,56)(34,61)(35,63)(36,62);
poly := sub<Sym(72)|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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope