Polytope of Type {6,4,12,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,12,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,134264)
Rank : 5
Schlafli Type : {6,4,12,2}
Number of vertices, edges, etc : 6, 12, 24, 12, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 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) :
2-fold quotients : {6,2,12,2}*576, {6,4,6,2}*576
3-fold quotients : {2,4,12,2}*384a, {6,4,4,2}*384
4-fold quotients : {3,2,12,2}*288, {6,2,6,2}*288
6-fold quotients : {2,2,12,2}*192, {2,4,6,2}*192a, {6,2,4,2}*192, {6,4,2,2}*192a
8-fold quotients : {3,2,6,2}*144, {6,2,3,2}*144
9-fold quotients : {2,4,4,2}*128
12-fold quotients : {3,2,4,2}*96, {2,2,6,2}*96, {6,2,2,2}*96
16-fold quotients : {3,2,3,2}*72
18-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
24-fold quotients : {2,2,3,2}*48, {3,2,2,2}*48
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)
(65,66)(68,69)(71,72);;
s1 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)
(55,65)(56,64)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72);;
s2 := ( 1,37)( 2,38)( 3,39)( 4,43)( 5,44)( 6,45)( 7,40)( 8,41)( 9,42)(10,46)
(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,55)(20,56)(21,57)
(22,61)(23,62)(24,63)(25,58)(26,59)(27,60)(28,64)(29,65)(30,66)(31,70)(32,71)
(33,72)(34,67)(35,68)(36,69);;
s3 := ( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)
(29,32)(30,33)(37,58)(38,59)(39,60)(40,55)(41,56)(42,57)(43,61)(44,62)(45,63)
(46,67)(47,68)(48,69)(49,64)(50,65)(51,66)(52,70)(53,71)(54,72);;
s4 := (73,74);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(74)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)
(62,63)(65,66)(68,69)(71,72);
s1 := Sym(74)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)
(28,29)(31,32)(34,35)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)
(45,54)(55,65)(56,64)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72);
s2 := Sym(74)!( 1,37)( 2,38)( 3,39)( 4,43)( 5,44)( 6,45)( 7,40)( 8,41)( 9,42)
(10,46)(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,55)(20,56)
(21,57)(22,61)(23,62)(24,63)(25,58)(26,59)(27,60)(28,64)(29,65)(30,66)(31,70)
(32,71)(33,72)(34,67)(35,68)(36,69);
s3 := Sym(74)!( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)
(28,31)(29,32)(30,33)(37,58)(38,59)(39,60)(40,55)(41,56)(42,57)(43,61)(44,62)
(45,63)(46,67)(47,68)(48,69)(49,64)(50,65)(51,66)(52,70)(53,71)(54,72);
s4 := Sym(74)!(73,74);
poly := sub<Sym(74)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope