Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*144c
if this polytope has a name.
Group : SmallGroup(144,154)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 12, 36, 6
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,6,2} of size 288
   {12,6,4} of size 576
   {12,6,4} of size 576
   {12,6,6} of size 864
   {12,6,6} of size 864
   {12,6,8} of size 1152
   {12,6,4} of size 1152
   {12,6,10} of size 1440
   {12,6,12} of size 1728
   {12,6,12} of size 1728
Vertex Figure Of :
   {2,12,6} of size 288
   {4,12,6} of size 576
   {6,12,6} of size 864
   {3,12,6} of size 864
   {6,12,6} of size 864
   {8,12,6} of size 1152
   {8,12,6} of size 1152
   {4,12,6} of size 1152
   {6,12,6} of size 1296
   {10,12,6} of size 1440
   {12,12,6} of size 1728
   {12,12,6} of size 1728
   {6,12,6} of size 1728
   {4,12,6} of size 1728
   {6,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*72b
   3-fold quotients : {4,6}*48a
   4-fold quotients : {6,3}*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 : {12,12}*288b, {24,6}*288c
   3-fold covers : {12,18}*432b, {12,6}*432c, {12,6}*432g
   4-fold covers : {24,12}*576a, {12,12}*576b, {24,12}*576b, {12,24}*576d, {12,24}*576f, {48,6}*576c, {12,6}*576e, {12,6}*576f
   5-fold covers : {60,6}*720a, {12,30}*720c
   6-fold covers : {12,36}*864b, {12,12}*864b, {24,18}*864b, {24,6}*864c, {24,6}*864f, {12,12}*864h
   7-fold covers : {84,6}*1008a, {12,42}*1008c
   8-fold covers : {12,24}*1152a, {24,12}*1152c, {24,24}*1152a, {24,24}*1152f, {24,24}*1152h, {24,24}*1152j, {12,48}*1152a, {48,12}*1152c, {12,48}*1152d, {48,12}*1152f, {12,12}*1152b, {24,12}*1152d, {12,24}*1152f, {96,6}*1152a, {12,12}*1152j, {12,12}*1152o, {24,6}*1152j, {24,6}*1152k, {12,6}*1152e, {24,6}*1152l, {12,12}*1152p, {12,12}*1152r, {12,6}*1152f, {24,6}*1152m
   9-fold covers : {36,18}*1296c, {12,18}*1296e, {12,54}*1296b, {12,18}*1296f, {12,18}*1296g, {12,18}*1296h, {12,6}*1296d, {36,6}*1296h, {36,6}*1296l, {12,18}*1296l, {12,6}*1296g, {12,6}*1296h, {12,6}*1296i, {12,6}*1296s
   10-fold covers : {120,6}*1440a, {60,12}*1440a, {12,60}*1440c, {24,30}*1440c
   11-fold covers : {132,6}*1584a, {12,66}*1584c
   12-fold covers : {24,36}*1728a, {24,12}*1728a, {12,36}*1728b, {12,12}*1728b, {24,36}*1728b, {24,12}*1728b, {12,72}*1728b, {12,24}*1728c, {12,72}*1728d, {12,24}*1728e, {48,18}*1728b, {48,6}*1728c, {48,6}*1728f, {12,24}*1728o, {24,12}*1728o, {12,24}*1728p, {24,12}*1728p, {12,12}*1728h, {12,18}*1728b, {12,18}*1728d, {12,6}*1728e, {12,6}*1728f, {12,12}*1728v, {12,6}*1728h, {12,6}*1728i
   13-fold covers : {156,6}*1872a, {12,78}*1872c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope