Polytope of Type {18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,4}*144a
Also Known As : {18,4|2}. if this polytope has another name.
Group : SmallGroup(144,41)
Rank : 3
Schlafli Type : {18,4}
Number of vertices, edges, etc : 18, 36, 4
Order of s₀s₁s₂ : 36
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {18,4,2} of size 288
   {18,4,4} of size 576
   {18,4,6} of size 864
   {18,4,3} of size 864
   {18,4,8} of size 1152
   {18,4,8} of size 1152
   {18,4,4} of size 1152
   {18,4,6} of size 1296
   {18,4,10} of size 1440
   {18,4,12} of size 1728
   {18,4,6} of size 1728
Vertex Figure Of :
   {2,18,4} of size 288
   {4,18,4} of size 576
   {4,18,4} of size 576
   {6,18,4} of size 864
   {6,18,4} of size 864
   {8,18,4} of size 1152
   {4,18,4} of size 1152
   {9,18,4} of size 1296
   {3,18,4} of size 1296
   {10,18,4} of size 1440
   {12,18,4} of size 1728
   {12,18,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {18,2}*72
   3-fold quotients : {6,4}*48a
   4-fold quotients : {9,2}*36
   6-fold quotients : {6,2}*24
   9-fold quotients : {2,4}*16
   12-fold quotients : {3,2}*12
   18-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {36,4}*288a, {18,8}*288
   3-fold covers : {54,4}*432a, {18,12}*432a, {18,12}*432b
   4-fold covers : {72,4}*576a, {36,4}*576a, {72,4}*576b, {36,8}*576a, {36,8}*576b, {18,16}*576, {18,4}*576b
   5-fold covers : {18,20}*720a, {90,4}*720a
   6-fold covers : {108,4}*864a, {54,8}*864, {18,24}*864a, {36,12}*864a, {36,12}*864b, {18,24}*864b
   7-fold covers : {18,28}*1008a, {126,4}*1008a
   8-fold covers : {36,8}*1152a, {72,4}*1152a, {72,8}*1152a, {72,8}*1152b, {72,8}*1152c, {72,8}*1152d, {36,16}*1152a, {144,4}*1152a, {36,16}*1152b, {144,4}*1152b, {36,4}*1152a, {72,4}*1152b, {36,8}*1152b, {18,32}*1152, {36,4}*1152d, {18,8}*1152f, {18,8}*1152g, {36,4}*1152e, {18,4}*1152b
   9-fold covers : {162,4}*1296a, {18,36}*1296a, {18,12}*1296a, {54,12}*1296a, {18,36}*1296c, {18,12}*1296e, {54,12}*1296b, {18,12}*1296l, {18,4}*1296b
   10-fold covers : {18,40}*1440, {36,20}*1440, {180,4}*1440a, {90,8}*1440
   11-fold covers : {18,44}*1584a, {198,4}*1584a
   12-fold covers : {216,4}*1728a, {108,4}*1728a, {216,4}*1728b, {108,8}*1728a, {108,8}*1728b, {54,16}*1728, {18,48}*1728a, {36,24}*1728a, {36,12}*1728a, {36,12}*1728b, {36,24}*1728b, {72,12}*1728a, {72,12}*1728b, {36,24}*1728c, {72,12}*1728c, {72,12}*1728d, {36,24}*1728d, {18,48}*1728b, {54,4}*1728b, {36,12}*1728c, {18,12}*1728b, {18,12}*1728c, {18,12}*1728d
   13-fold covers : {18,52}*1872a, {234,4}*1872a
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope