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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12,2}*576a
if this polytope has a name.
Group : SmallGroup(576,8545)
Rank : 5
Schlafli Type : {2,6,12,2}
Number of vertices, edges, etc : 2, 6, 36, 12, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,12,2,2} of size 1152
   {2,6,12,2,3} of size 1728
Vertex Figure Of :
   {2,2,6,12,2} of size 1152
   {3,2,6,12,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6,2}*288a
   3-fold quotients : {2,2,12,2}*192, {2,6,4,2}*192a
   6-fold quotients : {2,2,6,2}*96, {2,6,2,2}*96
   9-fold quotients : {2,2,4,2}*64
   12-fold quotients : {2,2,3,2}*48, {2,3,2,2}*48
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,12,4}*1152a, {2,12,12,2}*1152a, {4,6,12,2}*1152b, {2,6,24,2}*1152b
   3-fold covers : {2,18,12,2}*1728a, {2,6,36,2}*1728a, {2,6,12,2}*1728b, {2,6,12,6}*1728b, {2,6,12,6}*1728d, {6,6,12,2}*1728b, {6,6,12,2}*1728d, {2,6,12,2}*1728g
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)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74);;
s2 := ( 3,40)( 4,39)( 5,41)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,49)
(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,67)(22,66)(23,68)
(24,73)(25,72)(26,74)(27,70)(28,69)(29,71)(30,58)(31,57)(32,59)(33,64)(34,63)
(35,65)(36,61)(37,60)(38,62);;
s3 := ( 3,60)( 4,61)( 5,62)( 6,57)( 7,58)( 8,59)( 9,63)(10,64)(11,65)(12,69)
(13,70)(14,71)(15,66)(16,67)(17,68)(18,72)(19,73)(20,74)(21,42)(22,43)(23,44)
(24,39)(25,40)(26,41)(27,45)(28,46)(29,47)(30,51)(31,52)(32,53)(33,48)(34,49)
(35,50)(36,54)(37,55)(38,56);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope