Polytope of Type {2,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6}*288
if this polytope has a name.
Group : SmallGroup(288,1031)
Rank : 4
Schlafli Type : {2,4,6}
Number of vertices, edges, etc : 2, 12, 36, 18
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,6,2} of size 576
   {2,4,6,3} of size 864
   {2,4,6,4} of size 1152
   {2,4,6,6} of size 1728
   {2,4,6,6} of size 1728
Vertex Figure Of :
   {2,2,4,6} of size 576
   {3,2,4,6} of size 864
   {4,2,4,6} of size 1152
   {5,2,4,6} of size 1440
   {6,2,4,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,6}*144
   9-fold quotients : {2,4,2}*32
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,8,6}*576, {4,4,6}*576, {2,4,12}*576
   3-fold covers : {2,4,6}*864a, {2,12,6}*864e, {2,12,6}*864f, {6,4,6}*864a, {2,4,6}*864b, {2,12,6}*864h, {2,12,6}*864i
   4-fold covers : {4,4,12}*1152, {8,4,6}*1152a, {2,4,24}*1152a, {2,8,12}*1152a, {4,8,6}*1152a, {2,4,24}*1152b, {8,4,6}*1152b, {2,8,12}*1152b, {4,8,6}*1152b, {2,4,12}*1152, {4,4,6}*1152a, {2,16,6}*1152
   5-fold covers : {2,4,30}*1440, {10,4,6}*1440c, {2,20,6}*1440
   6-fold covers : {2,8,6}*1728a, {2,24,6}*1728d, {2,24,6}*1728e, {4,4,6}*1728a, {4,12,6}*1728h, {4,12,6}*1728i, {2,4,12}*1728b, {2,12,12}*1728d, {2,12,12}*1728e, {6,8,6}*1728b, {2,4,12}*1728c, {12,4,6}*1728a, {2,12,12}*1728i, {2,8,6}*1728b, {2,24,6}*1728g, {4,4,6}*1728c, {4,12,6}*1728p, {6,4,12}*1728b, {2,24,6}*1728h, {4,12,6}*1728q, {2,12,12}*1728k
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)
(34,37)(35,38)(39,48)(40,49)(41,50)(42,54)(43,55)(44,56)(45,51)(46,52)(47,53)
(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);;
s2 := ( 3,39)( 4,42)( 5,45)( 6,40)( 7,43)( 8,46)( 9,41)(10,44)(11,47)(12,48)
(13,51)(14,54)(15,49)(16,52)(17,55)(18,50)(19,53)(20,56)(21,57)(22,60)(23,63)
(24,58)(25,61)(26,64)(27,59)(28,62)(29,65)(30,66)(31,69)(32,72)(33,67)(34,70)
(35,73)(36,68)(37,71)(38,74);;
s3 := ( 3,31)( 4,30)( 5,32)( 6,37)( 7,36)( 8,38)( 9,34)(10,33)(11,35)(12,22)
(13,21)(14,23)(15,28)(16,27)(17,29)(18,25)(19,24)(20,26)(39,67)(40,66)(41,68)
(42,73)(43,72)(44,74)(45,70)(46,69)(47,71)(48,58)(49,57)(50,59)(51,64)(52,63)
(53,65)(54,61)(55,60)(56,62);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)
(33,36)(34,37)(35,38)(39,48)(40,49)(41,50)(42,54)(43,55)(44,56)(45,51)(46,52)
(47,53)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);
s2 := Sym(74)!( 3,39)( 4,42)( 5,45)( 6,40)( 7,43)( 8,46)( 9,41)(10,44)(11,47)
(12,48)(13,51)(14,54)(15,49)(16,52)(17,55)(18,50)(19,53)(20,56)(21,57)(22,60)
(23,63)(24,58)(25,61)(26,64)(27,59)(28,62)(29,65)(30,66)(31,69)(32,72)(33,67)
(34,70)(35,73)(36,68)(37,71)(38,74);
s3 := Sym(74)!( 3,31)( 4,30)( 5,32)( 6,37)( 7,36)( 8,38)( 9,34)(10,33)(11,35)
(12,22)(13,21)(14,23)(15,28)(16,27)(17,29)(18,25)(19,24)(20,26)(39,67)(40,66)
(41,68)(42,73)(43,72)(44,74)(45,70)(46,69)(47,71)(48,58)(49,57)(50,59)(51,64)
(52,63)(53,65)(54,61)(55,60)(56,62);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope