Polytope of Type {2,12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6,2}*576b
if this polytope has a name.
Group : SmallGroup(576,8545)
Rank : 5
Schlafli Type : {2,12,6,2}
Number of vertices, edges, etc : 2, 12, 36, 6, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,6,2,2} of size 1152
   {2,12,6,2,3} of size 1728
Vertex Figure Of :
   {2,2,12,6,2} of size 1152
   {3,2,12,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6,2}*288c
   3-fold quotients : {2,12,2,2}*192
   4-fold quotients : {2,3,6,2}*144
   6-fold quotients : {2,6,2,2}*96
   9-fold quotients : {2,4,2,2}*64
   12-fold quotients : {2,3,2,2}*48
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,6,2}*1152b, {2,12,12,2}*1152c, {2,12,6,4}*1152c, {2,24,6,2}*1152c
   3-fold covers : {2,36,6,2}*1728b, {2,12,6,2}*1728a, {2,12,6,6}*1728d, {6,12,6,2}*1728d, {6,12,6,2}*1728e, {2,12,6,2}*1728g
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,48)
(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,66)(22,68)(23,67)
(24,72)(25,74)(26,73)(27,69)(28,71)(29,70)(30,57)(31,59)(32,58)(33,63)(34,65)
(35,64)(36,60)(37,62)(38,61);;
s2 := ( 3,61)( 4,60)( 5,62)( 6,58)( 7,57)( 8,59)( 9,64)(10,63)(11,65)(12,70)
(13,69)(14,71)(15,67)(16,66)(17,68)(18,73)(19,72)(20,74)(21,43)(22,42)(23,44)
(24,40)(25,39)(26,41)(27,46)(28,45)(29,47)(30,52)(31,51)(32,53)(33,49)(34,48)
(35,50)(36,55)(37,54)(38,56);;
s3 := ( 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)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74);;
s4 := (75,76);;
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, 
s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
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(76)!(1,2);
s1 := Sym(76)!( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)
(12,48)(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,66)(22,68)
(23,67)(24,72)(25,74)(26,73)(27,69)(28,71)(29,70)(30,57)(31,59)(32,58)(33,63)
(34,65)(35,64)(36,60)(37,62)(38,61);
s2 := Sym(76)!( 3,61)( 4,60)( 5,62)( 6,58)( 7,57)( 8,59)( 9,64)(10,63)(11,65)
(12,70)(13,69)(14,71)(15,67)(16,66)(17,68)(18,73)(19,72)(20,74)(21,43)(22,42)
(23,44)(24,40)(25,39)(26,41)(27,46)(28,45)(29,47)(30,52)(31,51)(32,53)(33,49)
(34,48)(35,50)(36,55)(37,54)(38,56);
s3 := Sym(76)!( 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)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74);
s4 := Sym(76)!(75,76);
poly := sub<Sym(76)|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, s3*s4*s3*s4, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
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