# Polytope of Type {4,3,12}

Atlas Canonical Name : {4,3,12}*576
if this polytope has a name.
Group : SmallGroup(576,8660)
Rank : 4
Schlafli Type : {4,3,12}
Number of vertices, edges, etc : 4, 12, 36, 24
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,12,2} of size 1152
Vertex Figure Of :
{2,4,3,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,3,4}*192a
4-fold quotients : {4,3,6}*144
6-fold quotients : {4,3,4}*96
12-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,24}*1152, {4,3,12}*1152b, {4,6,12}*1152f, {4,6,12}*1152h
3-fold covers : {4,9,12}*1728, {4,3,12}*1728
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)(18,26)
(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)(37,45)
(38,46)(39,47)(40,48);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,33)(18,35)(19,34)(20,36)
(21,41)(22,43)(23,42)(24,44)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)
(32,48);;
s2 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,29)( 6,30)( 7,32)( 8,31)( 9,25)(10,26)
(11,28)(12,27)(13,21)(14,22)(15,24)(16,23)(35,36)(37,45)(38,46)(39,48)(40,47)
(43,44);;
s3 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,36)(18,35)
(19,34)(20,33)(21,40)(22,39)(23,38)(24,37)(25,44)(26,43)(27,42)(28,41)(29,48)
(30,47)(31,46)(32,45);;
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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(48)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)
(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)
(37,45)(38,46)(39,47)(40,48);
s1 := Sym(48)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,33)(18,35)(19,34)
(20,36)(21,41)(22,43)(23,42)(24,44)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)
(31,46)(32,48);
s2 := Sym(48)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,29)( 6,30)( 7,32)( 8,31)( 9,25)
(10,26)(11,28)(12,27)(13,21)(14,22)(15,24)(16,23)(35,36)(37,45)(38,46)(39,48)
(40,47)(43,44);
s3 := Sym(48)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,36)
(18,35)(19,34)(20,33)(21,40)(22,39)(23,38)(24,37)(25,44)(26,43)(27,42)(28,41)
(29,48)(30,47)(31,46)(32,45);
poly := sub<Sym(48)|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,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >;

References : None.
to this polytope