Polytope of Type {3,2,8,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {3,2,8,6}
Number of vertices, edges, etc : 3, 3, 16, 48, 12
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 : {3,2,8,3}*576, {3,2,4,6}*576
4-fold quotients : {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
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 := ( 4,30)( 5,31)( 6,29)( 7,28)( 8,34)( 9,35)(10,33)(11,32)(12,38)(13,39)
(14,37)(15,36)(16,42)(17,43)(18,41)(19,40)(20,46)(21,47)(22,45)(23,44)(24,50)
(25,51)(26,49)(27,48)(52,78)(53,79)(54,77)(55,76)(56,82)(57,83)(58,81)(59,80)
(60,86)(61,87)(62,85)(63,84)(64,90)(65,91)(66,89)(67,88)(68,94)(69,95)(70,93)
(71,92)(72,98)(73,99)(74,97)(75,96);;
s3 := ( 6, 8)( 7, 9)(10,11)(12,20)(13,21)(14,24)(15,25)(16,22)(17,23)(18,27)
(19,26)(28,29)(30,33)(31,32)(36,45)(37,44)(38,49)(39,48)(40,47)(41,46)(42,50)
(43,51)(54,56)(55,57)(58,59)(60,68)(61,69)(62,72)(63,73)(64,70)(65,71)(66,75)
(67,74)(76,77)(78,81)(79,80)(84,93)(85,92)(86,97)(87,96)(88,95)(89,94)(90,98)
(91,99);;
s4 := ( 4,60)( 5,61)( 6,63)( 7,62)( 8,66)( 9,67)(10,64)(11,65)(12,52)(13,53)
(14,55)(15,54)(16,58)(17,59)(18,56)(19,57)(20,68)(21,69)(22,71)(23,70)(24,74)
(25,75)(26,72)(27,73)(28,85)(29,84)(30,86)(31,87)(32,91)(33,90)(34,89)(35,88)
(36,77)(37,76)(38,78)(39,79)(40,83)(41,82)(42,81)(43,80)(44,93)(45,92)(46,94)
(47,95)(48,99)(49,98)(50,97)(51,96);;
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*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 4,30)( 5,31)( 6,29)( 7,28)( 8,34)( 9,35)(10,33)(11,32)(12,38)
(13,39)(14,37)(15,36)(16,42)(17,43)(18,41)(19,40)(20,46)(21,47)(22,45)(23,44)
(24,50)(25,51)(26,49)(27,48)(52,78)(53,79)(54,77)(55,76)(56,82)(57,83)(58,81)
(59,80)(60,86)(61,87)(62,85)(63,84)(64,90)(65,91)(66,89)(67,88)(68,94)(69,95)
(70,93)(71,92)(72,98)(73,99)(74,97)(75,96);
s3 := Sym(99)!( 6, 8)( 7, 9)(10,11)(12,20)(13,21)(14,24)(15,25)(16,22)(17,23)
(18,27)(19,26)(28,29)(30,33)(31,32)(36,45)(37,44)(38,49)(39,48)(40,47)(41,46)
(42,50)(43,51)(54,56)(55,57)(58,59)(60,68)(61,69)(62,72)(63,73)(64,70)(65,71)
(66,75)(67,74)(76,77)(78,81)(79,80)(84,93)(85,92)(86,97)(87,96)(88,95)(89,94)
(90,98)(91,99);
s4 := Sym(99)!( 4,60)( 5,61)( 6,63)( 7,62)( 8,66)( 9,67)(10,64)(11,65)(12,52)
(13,53)(14,55)(15,54)(16,58)(17,59)(18,56)(19,57)(20,68)(21,69)(22,71)(23,70)
(24,74)(25,75)(26,72)(27,73)(28,85)(29,84)(30,86)(31,87)(32,91)(33,90)(34,89)
(35,88)(36,77)(37,76)(38,78)(39,79)(40,83)(41,82)(42,81)(43,80)(44,93)(45,92)
(46,94)(47,95)(48,99)(49,98)(50,97)(51,96);
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*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3 >;
to this polytope