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# Polytope of Type {4,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*384d
if this polytope has a name.
Group : SmallGroup(384,17873)
Rank : 4
Schlafli Type : {4,12,4}
Number of vertices, edges, etc : 4, 24, 24, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,4,2} of size 768
Vertex Figure Of :
{2,4,12,4} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12,2}*192b, {4,6,4}*192c
4-fold quotients : {4,6,2}*96c
8-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,24,4}*768g, {4,24,4}*768h, {4,12,4}*768d, {4,24,4}*768k, {4,24,4}*768l, {4,12,8}*768c, {4,12,8}*768e, {4,12,4}*768f
3-fold covers : {4,36,4}*1152d, {4,12,12}*1152d, {4,12,12}*1152e
5-fold covers : {4,12,20}*1920b, {4,60,4}*1920d
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)
(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)
(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64)
(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)(77,79)(78,80)(81,83)(82,84)(85,87)
(86,88)(89,91)(90,92)(93,95)(94,96);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,73)
(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)
(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)
(72,92);;
s2 := ( 1,57)( 2,60)( 3,59)( 4,58)( 5,53)( 6,56)( 7,55)( 8,54)( 9,49)(10,52)
(11,51)(12,50)(13,69)(14,72)(15,71)(16,70)(17,65)(18,68)(19,67)(20,66)(21,61)
(22,64)(23,63)(24,62)(25,81)(26,84)(27,83)(28,82)(29,77)(30,80)(31,79)(32,78)
(33,73)(34,76)(35,75)(36,74)(37,93)(38,96)(39,95)(40,94)(41,89)(42,92)(43,91)
(44,90)(45,85)(46,88)(47,87)(48,86);;
s3 := (49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)
(59,71)(60,72)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)
(82,94)(83,95)(84,96);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;

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

```
References : None.
to this polytope