Polytope of Type {2,6,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,4}*384
if this polytope has a name.
Group : SmallGroup(384,18491)
Rank : 5
Schlafli Type : {2,6,4,4}
Number of vertices, edges, etc : 2, 6, 12, 8, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,4,4,2} of size 768
Vertex Figure Of :
{2,2,6,4,4} of size 768
{3,2,6,4,4} of size 1152
{5,2,6,4,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,2,4}*192, {2,6,4,2}*192a
3-fold quotients : {2,2,4,4}*128
4-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
6-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
8-fold quotients : {2,3,2,2}*48
12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,4,4}*768, {4,6,4,4}*768a, {2,6,4,8}*768a, {2,6,8,4}*768a, {2,6,4,8}*768b, {2,6,8,4}*768b, {2,6,4,4}*768a
3-fold covers : {2,18,4,4}*1152, {6,6,4,4}*1152a, {6,6,4,4}*1152b, {2,6,4,12}*1152, {2,6,12,4}*1152a, {2,6,12,4}*1152c
5-fold covers : {2,30,4,4}*1920, {10,6,4,4}*1920, {2,6,4,20}*1920, {2,6,20,4}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50);;
s2 := ( 3,16)( 4,15)( 5,17)( 6,19)( 7,18)( 8,20)( 9,22)(10,21)(11,23)(12,25)
(13,24)(14,26)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,46)(34,45)(35,47)
(36,49)(37,48)(38,50);;
s3 := (15,21)(16,22)(17,23)(18,24)(19,25)(20,26)(27,30)(28,31)(29,32)(33,36)
(34,37)(35,38)(39,48)(40,49)(41,50)(42,45)(43,46)(44,47);;
s4 := ( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)(12,36)
(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)
(24,48)(25,49)(26,50);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50);
s2 := Sym(50)!( 3,16)( 4,15)( 5,17)( 6,19)( 7,18)( 8,20)( 9,22)(10,21)(11,23)
(12,25)(13,24)(14,26)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,46)(34,45)
(35,47)(36,49)(37,48)(38,50);
s3 := Sym(50)!(15,21)(16,22)(17,23)(18,24)(19,25)(20,26)(27,30)(28,31)(29,32)
(33,36)(34,37)(35,38)(39,48)(40,49)(41,50)(42,45)(43,46)(44,47);
s4 := Sym(50)!( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)
(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)
(23,47)(24,48)(25,49)(26,50);
poly := sub<Sym(50)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope