Polytope of Type {3,2,4,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,6,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,136336)
Rank : 6
Schlafli Type : {3,2,4,6,4}
Number of vertices, edges, etc : 3, 3, 4, 12, 12, 4
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {3,2,2,6,4}*576a, {3,2,4,6,2}*576a
3-fold quotients : {3,2,4,2,4}*384
4-fold quotients : {3,2,2,6,2}*288
6-fold quotients : {3,2,2,2,4}*192, {3,2,4,2,2}*192
8-fold quotients : {3,2,2,3,2}*144
12-fold quotients : {3,2,2,2,2}*96
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)(10,58)(11,59)(12,60)(13,61)
(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)
(25,73)(26,74)(27,75)(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)(10,34)(11,36)(12,35)(13,37)
(14,39)(15,38)(16,46)(17,48)(18,47)(19,49)(20,51)(21,50)(22,40)(23,42)(24,41)
(25,43)(26,45)(27,44)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)(59,84)
(60,83)(61,85)(62,87)(63,86)(64,94)(65,96)(66,95)(67,97)(68,99)(69,98)(70,88)
(71,90)(72,89)(73,91)(74,93)(75,92);;
s4 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,26)(17,25)(18,27)(19,23)(20,22)(21,24)
(28,29)(31,32)(34,35)(37,38)(40,50)(41,49)(42,51)(43,47)(44,46)(45,48)(52,53)
(55,56)(58,59)(61,62)(64,74)(65,73)(66,75)(67,71)(68,70)(69,72)(76,77)(79,80)
(82,83)(85,86)(88,98)(89,97)(90,99)(91,95)(92,94)(93,96);;
s5 := ( 4,64)( 5,65)( 6,66)( 7,67)( 8,68)( 9,69)(10,70)(11,71)(12,72)(13,73)
(14,74)(15,75)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)
(25,61)(26,62)(27,63)(28,94)(29,95)(30,96)(31,97)(32,98)(33,99)(34,88)(35,89)
(36,90)(37,91)(38,92)(39,93)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,76)
(47,77)(48,78)(49,79)(50,80)(51,81);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5,
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)(10,58)(11,59)(12,60)
(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)
(24,72)(25,73)(26,74)(27,75)(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)(10,34)(11,36)(12,35)
(13,37)(14,39)(15,38)(16,46)(17,48)(18,47)(19,49)(20,51)(21,50)(22,40)(23,42)
(24,41)(25,43)(26,45)(27,44)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)
(59,84)(60,83)(61,85)(62,87)(63,86)(64,94)(65,96)(66,95)(67,97)(68,99)(69,98)
(70,88)(71,90)(72,89)(73,91)(74,93)(75,92);
s4 := Sym(99)!( 4, 5)( 7, 8)(10,11)(13,14)(16,26)(17,25)(18,27)(19,23)(20,22)
(21,24)(28,29)(31,32)(34,35)(37,38)(40,50)(41,49)(42,51)(43,47)(44,46)(45,48)
(52,53)(55,56)(58,59)(61,62)(64,74)(65,73)(66,75)(67,71)(68,70)(69,72)(76,77)
(79,80)(82,83)(85,86)(88,98)(89,97)(90,99)(91,95)(92,94)(93,96);
s5 := Sym(99)!( 4,64)( 5,65)( 6,66)( 7,67)( 8,68)( 9,69)(10,70)(11,71)(12,72)
(13,73)(14,74)(15,75)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,59)
(24,60)(25,61)(26,62)(27,63)(28,94)(29,95)(30,96)(31,97)(32,98)(33,99)(34,88)
(35,89)(36,90)(37,91)(38,92)(39,93)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)
(46,76)(47,77)(48,78)(49,79)(50,80)(51,81);
poly := sub<Sym(99)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope