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# Polytope of Type {4,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6}*384c
Also Known As : {{4,4}4,{4,6}3}. if this polytope has another name.
Group : SmallGroup(384,17948)
Rank : 4
Schlafli Type : {4,4,6}
Number of vertices, edges, etc : 8, 16, 24, 6
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,4,6,2} of size 768
Vertex Figure Of :
{2,4,4,6} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4,3}*192a
4-fold quotients : {2,4,6}*96b
8-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,6}*768d, {4,4,6}*768f
3-fold covers : {4,4,18}*1152c, {4,12,6}*1152d
5-fold covers : {4,20,6}*1920b, {4,4,30}*1920c
Permutation Representation (GAP) :
```s0 := ( 5, 7)( 6, 8)( 9,12)(10,11)(13,14)(15,16)(21,23)(22,24)(25,28)(26,27)
(29,30)(31,32)(37,39)(38,40)(41,44)(42,43)(45,46)(47,48)(53,55)(54,56)(57,60)
(58,59)(61,62)(63,64)(69,71)(70,72)(73,76)(74,75)(77,78)(79,80)(85,87)(86,88)
(89,92)(90,91)(93,94)(95,96);;
s1 := ( 1,57)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,49)(10,50)
(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,73)(18,74)(19,75)(20,76)(21,77)
(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)
(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,81)(42,82)(43,83)
(44,84)(45,85)(46,86)(47,87)(48,88);;
s2 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,33)(18,34)(19,36)(20,35)
(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,45)(30,46)(31,48)
(32,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,81)(66,82)(67,84)(68,83)
(69,89)(70,90)(71,92)(72,91)(73,85)(74,86)(75,88)(76,87)(77,93)(78,94)(79,96)
(80,95);;
s3 := ( 1,81)( 2,83)( 3,82)( 4,84)( 5,93)( 6,95)( 7,94)( 8,96)( 9,89)(10,91)
(11,90)(12,92)(13,85)(14,87)(15,86)(16,88)(17,65)(18,67)(19,66)(20,68)(21,77)
(22,79)(23,78)(24,80)(25,73)(26,75)(27,74)(28,76)(29,69)(30,71)(31,70)(32,72)
(33,49)(34,51)(35,50)(36,52)(37,61)(38,63)(39,62)(40,64)(41,57)(42,59)(43,58)
(44,60)(45,53)(46,55)(47,54)(48,56);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s1*s2*s3*s1*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(96)!( 5, 7)( 6, 8)( 9,12)(10,11)(13,14)(15,16)(21,23)(22,24)(25,28)
(26,27)(29,30)(31,32)(37,39)(38,40)(41,44)(42,43)(45,46)(47,48)(53,55)(54,56)
(57,60)(58,59)(61,62)(63,64)(69,71)(70,72)(73,76)(74,75)(77,78)(79,80)(85,87)
(86,88)(89,92)(90,91)(93,94)(95,96);
s1 := Sym(96)!( 1,57)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,49)
(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,73)(18,74)(19,75)(20,76)
(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)
(32,72)(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,81)(42,82)
(43,83)(44,84)(45,85)(46,86)(47,87)(48,88);
s2 := Sym(96)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,33)(18,34)(19,36)
(20,35)(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,45)(30,46)
(31,48)(32,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,81)(66,82)(67,84)
(68,83)(69,89)(70,90)(71,92)(72,91)(73,85)(74,86)(75,88)(76,87)(77,93)(78,94)
(79,96)(80,95);
s3 := Sym(96)!( 1,81)( 2,83)( 3,82)( 4,84)( 5,93)( 6,95)( 7,94)( 8,96)( 9,89)
(10,91)(11,90)(12,92)(13,85)(14,87)(15,86)(16,88)(17,65)(18,67)(19,66)(20,68)
(21,77)(22,79)(23,78)(24,80)(25,73)(26,75)(27,74)(28,76)(29,69)(30,71)(31,70)
(32,72)(33,49)(34,51)(35,50)(36,52)(37,61)(38,63)(39,62)(40,64)(41,57)(42,59)
(43,58)(44,60)(45,53)(46,55)(47,54)(48,56);
poly := sub<Sym(96)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s1*s2*s3*s1*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

```
References : None.
to this polytope