Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*576a
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 24, 72, 12
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,6,2} of size 1152
Vertex Figure Of :
   {2,2,12,6} of size 1152
   {3,2,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,6}*288d
   3-fold quotients : {2,4,6}*192
   4-fold quotients : {2,6,6}*144a
   6-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   12-fold quotients : {2,4,3}*48, {2,2,6}*48, {2,6,2}*48
   24-fold quotients : {2,2,3}*24, {2,3,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,12}*1152f, {2,12,6}*1152b, {4,12,6}*1152g, {2,24,6}*1152c, {2,24,6}*1152e, {2,12,12}*1152k
   3-fold covers : {2,36,6}*1728, {2,12,18}*1728a, {2,12,6}*1728b, {6,12,6}*1728e, {6,12,6}*1728g, {2,12,6}*1728c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope