Polytope of Type {6,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*288a
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 12, 72, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,12,2} of size 576
   {6,12,4} of size 1152
   {6,12,4} of size 1152
   {6,12,6} of size 1728
   {6,12,6} of size 1728
   {6,12,6} of size 1728
Vertex Figure Of :
   {2,6,12} of size 576
   {3,6,12} of size 1152
   {4,6,12} of size 1152
   {4,6,12} of size 1152
   {6,6,12} of size 1728
   {6,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*144d
   3-fold quotients : {6,4}*96
   4-fold quotients : {6,6}*72a
   6-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   12-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
   24-fold quotients : {2,3}*12, {3,2}*12
   36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12}*576d, {6,12}*576b, {6,24}*576c, {6,24}*576e, {12,12}*576j
   3-fold covers : {6,36}*864, {18,12}*864a, {6,12}*864b, {6,12}*864c
   4-fold covers : {6,24}*1152c, {12,24}*1152i, {12,24}*1152k, {6,24}*1152d, {6,12}*1152b, {6,24}*1152e, {24,12}*1152o, {24,12}*1152q, {6,24}*1152h, {6,12}*1152d, {12,12}*1152h, {12,12}*1152k, {12,24}*1152u, {12,24}*1152v, {24,12}*1152w, {24,12}*1152x, {12,12}*1152t
   5-fold covers : {30,12}*1440a, {6,60}*1440d
   6-fold covers : {12,36}*1728c, {6,36}*1728b, {6,72}*1728b, {6,72}*1728c, {12,36}*1728d, {36,12}*1728e, {18,12}*1728c, {12,12}*1728j, {6,12}*1728b, {18,24}*1728c, {6,24}*1728c, {18,24}*1728e, {6,24}*1728e, {36,12}*1728h, {12,12}*1728o, {6,24}*1728f, {6,24}*1728g, {12,12}*1728v, {6,12}*1728i, {12,12}*1728x
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 2.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {6}*12
         4 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 2.
      12 facets:
         12 of {6}*12
      6 vertex figures:
         6 of {12}*24

Permutation Representation (GAP) : 
s0 := ( 2, 3)( 6, 7)(10,11)(13,25)(14,27)(15,26)(16,28)(17,29)(18,31)(19,30)(20,32)(21,33)(22,35)(23,34)(24,36)(38,39)(42,43)(46,47)(49,61)(50,63)(51,62)(52,64)(53,65)(54,67)(55,66)(56,68)(57,69)(58,71)(59,70)(60,72);;
s1 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(63,64)(65,69)(66,70)(67,72)(68,71);;
s2 := ( 1,44)( 2,43)( 3,42)( 4,41)( 5,40)( 6,39)( 7,38)( 8,37)( 9,48)(10,47)(11,46)(12,45)(13,56)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,60)(22,59)(23,58)(24,57)(25,68)(26,67)(27,66)(28,65)(29,64)(30,63)(31,62)(32,61)(33,72)(34,71)(35,70)(36,69);;
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*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(72)!( 2, 3)( 6, 7)(10,11)(13,25)(14,27)(15,26)(16,28)(17,29)(18,31)(19,30)(20,32)(21,33)(22,35)(23,34)(24,36)(38,39)(42,43)(46,47)(49,61)(50,63)(51,62)(52,64)(53,65)(54,67)(55,66)(56,68)(57,69)(58,71)(59,70)(60,72);
s1 := Sym(72)!( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(63,64)(65,69)(66,70)(67,72)(68,71);
s2 := Sym(72)!( 1,44)( 2,43)( 3,42)( 4,41)( 5,40)( 6,39)( 7,38)( 8,37)( 9,48)(10,47)(11,46)(12,45)(13,56)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,60)(22,59)(23,58)(24,57)(25,68)(26,67)(27,66)(28,65)(29,64)(30,63)(31,62)(32,61)(33,72)(34,71)(35,70)(36,69);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References : None.
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