Polytope of Type {3,2,4,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 5
Schlafli Type : {3,2,4,12}
Number of vertices, edges, etc : 3, 3, 8, 48, 24
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 : {3,2,4,12}*576b, {3,2,4,12}*576c, {3,2,4,6}*576
4-fold quotients : {3,2,2,12}*288, {3,2,4,3}*288, {3,2,4,6}*288b, {3,2,4,6}*288c
8-fold quotients : {3,2,4,3}*144, {3,2,2,6}*144
12-fold quotients : {3,2,2,4}*96
16-fold quotients : {3,2,2,3}*72
24-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,53)( 5,52)( 6,55)( 7,54)( 8,57)( 9,56)(10,59)(11,58)(12,61)(13,60)
(14,63)(15,62)(16,65)(17,64)(18,67)(19,66)(20,69)(21,68)(22,71)(23,70)(24,73)
(25,72)(26,75)(27,74)(28,77)(29,76)(30,79)(31,78)(32,81)(33,80)(34,83)(35,82)
(36,85)(37,84)(38,87)(39,86)(40,89)(41,88)(42,91)(43,90)(44,93)(45,92)(46,95)
(47,94)(48,97)(49,96)(50,99)(51,98);;
s3 := ( 5, 6)( 8,12)( 9,14)(10,13)(11,15)(17,18)(20,24)(21,26)(22,25)(23,27)
(28,40)(29,42)(30,41)(31,43)(32,48)(33,50)(34,49)(35,51)(36,44)(37,46)(38,45)
(39,47)(53,54)(56,60)(57,62)(58,61)(59,63)(65,66)(68,72)(69,74)(70,73)(71,75)
(76,88)(77,90)(78,89)(79,91)(80,96)(81,98)(82,97)(83,99)(84,92)(85,94)(86,93)
(87,95);;
s4 := ( 4,32)( 5,33)( 6,35)( 7,34)( 8,28)( 9,29)(10,31)(11,30)(12,36)(13,37)
(14,39)(15,38)(16,44)(17,45)(18,47)(19,46)(20,40)(21,41)(22,43)(23,42)(24,48)
(25,49)(26,51)(27,50)(52,80)(53,81)(54,83)(55,82)(56,76)(57,77)(58,79)(59,78)
(60,84)(61,85)(62,87)(63,86)(64,92)(65,93)(66,95)(67,94)(68,88)(69,89)(70,91)
(71,90)(72,96)(73,97)(74,99)(75,98);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 4,53)( 5,52)( 6,55)( 7,54)( 8,57)( 9,56)(10,59)(11,58)(12,61)
(13,60)(14,63)(15,62)(16,65)(17,64)(18,67)(19,66)(20,69)(21,68)(22,71)(23,70)
(24,73)(25,72)(26,75)(27,74)(28,77)(29,76)(30,79)(31,78)(32,81)(33,80)(34,83)
(35,82)(36,85)(37,84)(38,87)(39,86)(40,89)(41,88)(42,91)(43,90)(44,93)(45,92)
(46,95)(47,94)(48,97)(49,96)(50,99)(51,98);
s3 := Sym(99)!( 5, 6)( 8,12)( 9,14)(10,13)(11,15)(17,18)(20,24)(21,26)(22,25)
(23,27)(28,40)(29,42)(30,41)(31,43)(32,48)(33,50)(34,49)(35,51)(36,44)(37,46)
(38,45)(39,47)(53,54)(56,60)(57,62)(58,61)(59,63)(65,66)(68,72)(69,74)(70,73)
(71,75)(76,88)(77,90)(78,89)(79,91)(80,96)(81,98)(82,97)(83,99)(84,92)(85,94)
(86,93)(87,95);
s4 := Sym(99)!( 4,32)( 5,33)( 6,35)( 7,34)( 8,28)( 9,29)(10,31)(11,30)(12,36)
(13,37)(14,39)(15,38)(16,44)(17,45)(18,47)(19,46)(20,40)(21,41)(22,43)(23,42)
(24,48)(25,49)(26,51)(27,50)(52,80)(53,81)(54,83)(55,82)(56,76)(57,77)(58,79)
(59,78)(60,84)(61,85)(62,87)(63,86)(64,92)(65,93)(66,95)(67,94)(68,88)(69,89)
(70,91)(71,90)(72,96)(73,97)(74,99)(75,98);
poly := sub<Sym(99)|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, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope