Polytope of Type {6,12,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,2}*288b
if this polytope has a name.
Group : SmallGroup(288,951)
Rank : 4
Schlafli Type : {6,12,2}
Number of vertices, edges, etc : 6, 36, 12, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,12,2,2} of size 576
{6,12,2,3} of size 864
{6,12,2,4} of size 1152
{6,12,2,5} of size 1440
{6,12,2,6} of size 1728
Vertex Figure Of :
{2,6,12,2} of size 576
{3,6,12,2} of size 864
{4,6,12,2} of size 1152
{6,6,12,2} of size 1728
{6,6,12,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,6,2}*144b
3-fold quotients : {2,12,2}*96
4-fold quotients : {6,3,2}*72
6-fold quotients : {2,6,2}*48
9-fold quotients : {2,4,2}*32
12-fold quotients : {2,3,2}*24
18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,12,4}*576b, {6,24,2}*576b, {12,12,2}*576b
3-fold covers : {6,36,2}*864b, {6,12,2}*864a, {6,12,6}*864c, {6,12,6}*864e, {6,12,2}*864g
4-fold covers : {12,12,4}*1152a, {6,12,8}*1152a, {6,24,4}*1152b, {12,24,2}*1152b, {24,12,2}*1152c, {6,12,8}*1152d, {6,24,4}*1152e, {12,24,2}*1152e, {24,12,2}*1152f, {6,12,4}*1152a, {12,12,2}*1152b, {6,48,2}*1152c, {6,12,4}*1152f, {12,12,2}*1152g, {6,12,2}*1152a
5-fold covers : {6,12,10}*1440b, {30,12,2}*1440a, {6,60,2}*1440c
6-fold covers : {6,36,4}*1728b, {6,12,4}*1728a, {6,72,2}*1728b, {6,24,2}*1728a, {12,36,2}*1728b, {12,12,2}*1728b, {6,24,6}*1728c, {6,24,6}*1728e, {6,24,2}*1728f, {6,12,12}*1728d, {6,12,12}*1728f, {12,12,6}*1728c, {12,12,6}*1728e, {12,12,2}*1728h, {6,12,4}*1728j
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)
(65,66)(68,69)(71,72);;
s1 := ( 1,38)( 2,37)( 3,39)( 4,44)( 5,43)( 6,45)( 7,41)( 8,40)( 9,42)(10,47)
(11,46)(12,48)(13,53)(14,52)(15,54)(16,50)(17,49)(18,51)(19,65)(20,64)(21,66)
(22,71)(23,70)(24,72)(25,68)(26,67)(27,69)(28,56)(29,55)(30,57)(31,62)(32,61)
(33,63)(34,59)(35,58)(36,60);;
s2 := ( 1,58)( 2,60)( 3,59)( 4,55)( 5,57)( 6,56)( 7,61)( 8,63)( 9,62)(10,67)
(11,69)(12,68)(13,64)(14,66)(15,65)(16,70)(17,72)(18,71)(19,40)(20,42)(21,41)
(22,37)(23,39)(24,38)(25,43)(26,45)(27,44)(28,49)(29,51)(30,50)(31,46)(32,48)
(33,47)(34,52)(35,54)(36,53);;
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,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(74)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)
(62,63)(65,66)(68,69)(71,72);
s1 := Sym(74)!( 1,38)( 2,37)( 3,39)( 4,44)( 5,43)( 6,45)( 7,41)( 8,40)( 9,42)
(10,47)(11,46)(12,48)(13,53)(14,52)(15,54)(16,50)(17,49)(18,51)(19,65)(20,64)
(21,66)(22,71)(23,70)(24,72)(25,68)(26,67)(27,69)(28,56)(29,55)(30,57)(31,62)
(32,61)(33,63)(34,59)(35,58)(36,60);
s2 := Sym(74)!( 1,58)( 2,60)( 3,59)( 4,55)( 5,57)( 6,56)( 7,61)( 8,63)( 9,62)
(10,67)(11,69)(12,68)(13,64)(14,66)(15,65)(16,70)(17,72)(18,71)(19,40)(20,42)
(21,41)(22,37)(23,39)(24,38)(25,43)(26,45)(27,44)(28,49)(29,51)(30,50)(31,46)
(32,48)(33,47)(34,52)(35,54)(36,53);
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 >;
to this polytope