Polytope of Type {3,2,8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97531)
Rank : 5
Schlafli Type : {3,2,8,12}
Number of vertices, edges, etc : 3, 3, 8, 48, 12
Order of s0s1s2s3s4 : 24
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}*576a, {3,2,8,6}*576
3-fold quotients : {3,2,8,4}*384a
4-fold quotients : {3,2,2,12}*288, {3,2,4,6}*288a
6-fold quotients : {3,2,4,4}*192, {3,2,8,2}*192
8-fold quotients : {3,2,2,6}*144
12-fold quotients : {3,2,2,4}*96, {3,2,4,2}*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 := ( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,61)(11,62)(12,63)(13,58)
(14,59)(15,60)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,73)(23,74)(24,75)
(25,70)(26,71)(27,72)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,76)(35,77)
(36,78)(37,79)(38,80)(39,81)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,88)
(47,89)(48,90)(49,91)(50,92)(51,93);;
s3 := ( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,37)(11,39)(12,38)(13,34)
(14,36)(15,35)(16,40)(17,42)(18,41)(19,43)(20,45)(21,44)(22,49)(23,51)(24,50)
(25,46)(26,48)(27,47)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,85)(59,87)
(60,86)(61,82)(62,84)(63,83)(64,88)(65,90)(66,89)(67,91)(68,93)(69,92)(70,97)
(71,99)(72,98)(73,94)(74,96)(75,95);;
s4 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,41)(29,40)
(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(37,50)(38,49)(39,51)(52,53)
(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(76,89)(77,88)(78,90)(79,92)
(80,91)(81,93)(82,95)(83,94)(84,96)(85,98)(86,97)(87,99);;
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*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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)!( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,61)(11,62)(12,63)
(13,58)(14,59)(15,60)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,73)(23,74)
(24,75)(25,70)(26,71)(27,72)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,76)
(35,77)(36,78)(37,79)(38,80)(39,81)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)
(46,88)(47,89)(48,90)(49,91)(50,92)(51,93);
s3 := Sym(99)!( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,37)(11,39)(12,38)
(13,34)(14,36)(15,35)(16,40)(17,42)(18,41)(19,43)(20,45)(21,44)(22,49)(23,51)
(24,50)(25,46)(26,48)(27,47)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,85)
(59,87)(60,86)(61,82)(62,84)(63,83)(64,88)(65,90)(66,89)(67,91)(68,93)(69,92)
(70,97)(71,99)(72,98)(73,94)(74,96)(75,95);
s4 := Sym(99)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,41)
(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(37,50)(38,49)(39,51)
(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(76,89)(77,88)(78,90)
(79,92)(80,91)(81,93)(82,95)(83,94)(84,96)(85,98)(86,97)(87,99);
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*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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