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# Polytope of Type {2,24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,6}*576b
if this polytope has a name.
Group : SmallGroup(576,6554)
Rank : 4
Schlafli Type : {2,24,6}
Number of vertices, edges, etc : 2, 24, 72, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,24,6,2} of size 1152
{2,24,6,3} of size 1728
Vertex Figure Of :
{2,2,24,6} of size 1152
{3,2,24,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,12,6}*288b
3-fold quotients : {2,24,2}*192
4-fold quotients : {2,6,6}*144c
6-fold quotients : {2,12,2}*96
8-fold quotients : {2,3,6}*72
9-fold quotients : {2,8,2}*64
12-fold quotients : {2,6,2}*48
18-fold quotients : {2,4,2}*32
24-fold quotients : {2,3,2}*24
36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,24,6}*1152b, {2,24,12}*1152b, {2,48,6}*1152c
3-fold covers : {2,72,6}*1728b, {2,24,6}*1728a, {6,24,6}*1728d, {6,24,6}*1728e, {2,24,6}*1728f
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(21,30)(22,32)
(23,31)(24,36)(25,38)(26,37)(27,33)(28,35)(29,34)(39,57)(40,59)(41,58)(42,63)
(43,65)(44,64)(45,60)(46,62)(47,61)(48,66)(49,68)(50,67)(51,72)(52,74)(53,73)
(54,69)(55,71)(56,70);;
s2 := ( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)(12,52)
(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,70)(22,69)(23,71)
(24,67)(25,66)(26,68)(27,73)(28,72)(29,74)(30,61)(31,60)(32,62)(33,58)(34,57)
(35,59)(36,64)(37,63)(38,65);;
s3 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74);;
poly := Group([s0,s1,s2,s3]);;

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

```
Permutation Representation (Magma) :
```s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(21,30)
(22,32)(23,31)(24,36)(25,38)(26,37)(27,33)(28,35)(29,34)(39,57)(40,59)(41,58)
(42,63)(43,65)(44,64)(45,60)(46,62)(47,61)(48,66)(49,68)(50,67)(51,72)(52,74)
(53,73)(54,69)(55,71)(56,70);
s2 := Sym(74)!( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)
(12,52)(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,70)(22,69)
(23,71)(24,67)(25,66)(26,68)(27,73)(28,72)(29,74)(30,61)(31,60)(32,62)(33,58)
(34,57)(35,59)(36,64)(37,63)(38,65);
s3 := Sym(74)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74);
poly := sub<Sym(74)|s0,s1,s2,s3>;

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

```

to this polytope