Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*1728c
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 72, 216, 36
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   3-fold quotients : {2,12,6}*576a, {2,12,6}*576b
   4-fold quotients : {2,6,6}*432d
   6-fold quotients : {2,12,3}*288, {2,12,6}*288d
   9-fold quotients : {2,4,6}*192
   12-fold quotients : {2,6,6}*144a, {2,6,6}*144b, {2,6,6}*144c
   18-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   24-fold quotients : {2,3,6}*72, {2,6,3}*72
   36-fold quotients : {2,4,3}*48, {2,2,6}*48, {2,6,2}*48
   72-fold quotients : {2,2,3}*24, {2,3,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,29)(16,30)(17,27)(18,28)
(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32);;
s2 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,15)( 8,17)( 9,16)(10,18)(11,23)(12,25)
(13,24)(14,26)(27,31)(28,33)(29,32)(30,34)(36,37);;
s3 := ( 4, 6)( 7,11)( 8,14)( 9,13)(10,12)(16,18)(19,23)(20,26)(21,25)(22,24)
(28,30)(31,35)(32,38)(33,37)(34,36);;
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*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,29)(16,30)(17,27)
(18,28)(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32);
s2 := Sym(38)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,15)( 8,17)( 9,16)(10,18)(11,23)
(12,25)(13,24)(14,26)(27,31)(28,33)(29,32)(30,34)(36,37);
s3 := Sym(38)!( 4, 6)( 7,11)( 8,14)( 9,13)(10,12)(16,18)(19,23)(20,26)(21,25)
(22,24)(28,30)(31,35)(32,38)(33,37)(34,36);
poly := sub<Sym(38)|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*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope