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# Polytope of Type {12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2}*576a
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 4
Schlafli Type : {12,6,2}
Number of vertices, edges, etc : 24, 72, 12, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,6,2,2} of size 1152
{12,6,2,3} of size 1728
Vertex Figure Of :
{2,12,6,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,6,2}*288d
3-fold quotients : {4,6,2}*192
4-fold quotients : {6,6,2}*144a
6-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
12-fold quotients : {4,3,2}*48, {2,6,2}*48, {6,2,2}*48
24-fold quotients : {2,3,2}*24, {3,2,2}*24
36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,12,2}*1152f, {12,6,2}*1152b, {12,6,4}*1152b, {24,6,2}*1152c, {24,6,2}*1152e, {12,12,2}*1152k
3-fold covers : {36,6,2}*1728, {12,18,2}*1728a, {12,6,2}*1728b, {12,6,6}*1728a, {12,6,6}*1728c, {12,6,2}*1728c
Permutation Representation (GAP) :
s0 := ( 1, 2)( 3, 4)( 5,10)( 6, 9)( 7,12)( 8,11)(13,14)(15,16)(17,22)(18,21)
(19,24)(20,23)(25,26)(27,28)(29,34)(30,33)(31,36)(32,35)(37,38)(39,40)(41,46)
(42,45)(43,48)(44,47)(49,50)(51,52)(53,58)(54,57)(55,60)(56,59)(61,62)(63,64)
(65,70)(66,69)(67,72)(68,71);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,29)(14,31)(15,30)(16,32)(17,25)
(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(37,41)(38,43)(39,42)(40,44)
(46,47)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)(58,71)
(59,70)(60,72);;
s2 := ( 1,49)( 2,50)( 3,52)( 4,51)( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)(10,58)
(11,60)(12,59)(13,37)(14,38)(15,40)(16,39)(17,41)(18,42)(19,44)(20,43)(21,45)
(22,46)(23,48)(24,47)(25,61)(26,62)(27,64)(28,63)(29,65)(30,66)(31,68)(32,67)
(33,69)(34,70)(35,72)(36,71);;
s3 := (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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

to this polytope