Polytope of Type {4,18}

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

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

Permutation Representation (Magma) :

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

References : None.
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