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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,47319)
Rank : 5
Schlafli Type : {12,6,2,6}
Number of vertices, edges, etc : 12, 36, 6, 6, 6
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6,2,3}*864a, {6,6,2,6}*864a
   3-fold quotients : {12,2,2,6}*576, {12,6,2,2}*576a, {4,6,2,6}*576a
   4-fold quotients : {6,6,2,3}*432a
   6-fold quotients : {12,2,2,3}*288, {4,6,2,3}*288a, {2,6,2,6}*288, {6,2,2,6}*288, {6,6,2,2}*288a
   9-fold quotients : {12,2,2,2}*192, {4,2,2,6}*192, {4,6,2,2}*192a
   12-fold quotients : {2,3,2,6}*144, {2,6,2,3}*144, {3,2,2,6}*144, {6,2,2,3}*144
   18-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96, {2,6,2,2}*96, {6,2,2,2}*96
   24-fold quotients : {2,3,2,3}*72, {3,2,2,3}*72
   27-fold quotients : {4,2,2,2}*64
   36-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48, {3,2,2,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,37)( 2,38)( 3,39)( 4,43)( 5,44)( 6,45)( 7,40)( 8,41)( 9,42)(10,46)
(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,64)(20,65)(21,66)
(22,70)(23,71)(24,72)(25,67)(26,68)(27,69)(28,55)(29,56)(30,57)(31,61)(32,62)
(33,63)(34,58)(35,59)(36,60);;
s1 := ( 1,58)( 2,60)( 3,59)( 4,55)( 5,57)( 6,56)( 7,61)( 8,63)( 9,62)(10,67)
(11,69)(12,68)(13,64)(14,66)(15,65)(16,70)(17,72)(18,71)(19,40)(20,42)(21,41)
(22,37)(23,39)(24,38)(25,43)(26,45)(27,44)(28,49)(29,51)(30,50)(31,46)(32,48)
(33,47)(34,52)(35,54)(36,53);;
s2 := ( 1, 2)( 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);;
s3 := (75,76)(77,78);;
s4 := (73,77)(74,75)(76,78);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(78)!( 1,37)( 2,38)( 3,39)( 4,43)( 5,44)( 6,45)( 7,40)( 8,41)( 9,42)
(10,46)(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,64)(20,65)
(21,66)(22,70)(23,71)(24,72)(25,67)(26,68)(27,69)(28,55)(29,56)(30,57)(31,61)
(32,62)(33,63)(34,58)(35,59)(36,60);
s1 := Sym(78)!( 1,58)( 2,60)( 3,59)( 4,55)( 5,57)( 6,56)( 7,61)( 8,63)( 9,62)
(10,67)(11,69)(12,68)(13,64)(14,66)(15,65)(16,70)(17,72)(18,71)(19,40)(20,42)
(21,41)(22,37)(23,39)(24,38)(25,43)(26,45)(27,44)(28,49)(29,51)(30,50)(31,46)
(32,48)(33,47)(34,52)(35,54)(36,53);
s2 := Sym(78)!( 1, 2)( 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);
s3 := Sym(78)!(75,76)(77,78);
s4 := Sym(78)!(73,77)(74,75)(76,78);
poly := sub<Sym(78)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope