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# Polytope of Type {24,6}

Atlas Canonical Name : {24,6}*288c
if this polytope has a name.
Group : SmallGroup(288,574)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 24, 72, 6
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{24,6,2} of size 576
{24,6,4} of size 1152
{24,6,4} of size 1152
{24,6,6} of size 1728
{24,6,6} of size 1728
Vertex Figure Of :
{2,24,6} of size 576
{4,24,6} of size 1152
{4,24,6} of size 1152
{6,24,6} of size 1728
{3,24,6} of size 1728
{6,24,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,6}*144c
3-fold quotients : {8,6}*96
4-fold quotients : {6,6}*72b
6-fold quotients : {4,6}*48a
8-fold quotients : {6,3}*36
9-fold quotients : {8,2}*32
12-fold quotients : {2,6}*24
18-fold quotients : {4,2}*16
24-fold quotients : {2,3}*12
36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,12}*576b, {48,6}*576c
3-fold covers : {24,18}*864b, {24,6}*864c, {24,6}*864f
4-fold covers : {24,12}*1152c, {24,24}*1152f, {24,24}*1152h, {48,12}*1152c, {48,12}*1152f, {96,6}*1152a, {24,6}*1152j, {24,6}*1152k
5-fold covers : {120,6}*1440a, {24,30}*1440c
6-fold covers : {24,36}*1728b, {24,12}*1728b, {48,18}*1728b, {48,6}*1728c, {48,6}*1728f, {24,12}*1728o
Permutation Representation (GAP) :
```s0 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)(22,34)
(23,35)(24,36)(25,31)(26,32)(27,33)(37,55)(38,56)(39,57)(40,61)(41,62)(42,63)
(43,58)(44,59)(45,60)(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)(53,68)
(54,69);;
s1 := ( 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);;
s2 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)(22,26)
(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,38)(40,44)(41,43)(42,45)(46,47)
(49,53)(50,52)(51,54)(55,56)(58,62)(59,61)(60,63)(64,65)(67,71)(68,70)
(69,72);;
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*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope