Polytope of Type {8,6,2,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,2,3}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {8,6,2,3}
Number of vertices, edges, etc : 16, 48, 12, 3, 3
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 : {8,3,2,3}*576, {4,6,2,3}*576
4-fold quotients : {4,3,2,3}*288, {4,6,2,3}*288b, {4,6,2,3}*288c
8-fold quotients : {4,3,2,3}*144, {2,6,2,3}*144
16-fold quotients : {2,3,2,3}*72
24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,27)( 2,28)( 3,26)( 4,25)( 5,31)( 6,32)( 7,30)( 8,29)( 9,35)(10,36)
(11,34)(12,33)(13,39)(14,40)(15,38)(16,37)(17,43)(18,44)(19,42)(20,41)(21,47)
(22,48)(23,46)(24,45)(49,75)(50,76)(51,74)(52,73)(53,79)(54,80)(55,78)(56,77)
(57,83)(58,84)(59,82)(60,81)(61,87)(62,88)(63,86)(64,85)(65,91)(66,92)(67,90)
(68,89)(69,95)(70,96)(71,94)(72,93);;
s1 := ( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)(15,24)
(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)(39,47)
(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)(63,72)
(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)(87,95)
(88,96);;
s2 := ( 1,57)( 2,58)( 3,60)( 4,59)( 5,63)( 6,64)( 7,61)( 8,62)( 9,49)(10,50)
(11,52)(12,51)(13,55)(14,56)(15,53)(16,54)(17,65)(18,66)(19,68)(20,67)(21,71)
(22,72)(23,69)(24,70)(25,82)(26,81)(27,83)(28,84)(29,88)(30,87)(31,86)(32,85)
(33,74)(34,73)(35,75)(36,76)(37,80)(38,79)(39,78)(40,77)(41,90)(42,89)(43,91)
(44,92)(45,96)(46,95)(47,94)(48,93);;
s3 := (98,99);;
s4 := (97,98);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(99)!( 1,27)( 2,28)( 3,26)( 4,25)( 5,31)( 6,32)( 7,30)( 8,29)( 9,35)
(10,36)(11,34)(12,33)(13,39)(14,40)(15,38)(16,37)(17,43)(18,44)(19,42)(20,41)
(21,47)(22,48)(23,46)(24,45)(49,75)(50,76)(51,74)(52,73)(53,79)(54,80)(55,78)
(56,77)(57,83)(58,84)(59,82)(60,81)(61,87)(62,88)(63,86)(64,85)(65,91)(66,92)
(67,90)(68,89)(69,95)(70,96)(71,94)(72,93);
s1 := Sym(99)!( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)
(15,24)(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)
(39,47)(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)
(63,72)(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)
(87,95)(88,96);
s2 := Sym(99)!( 1,57)( 2,58)( 3,60)( 4,59)( 5,63)( 6,64)( 7,61)( 8,62)( 9,49)
(10,50)(11,52)(12,51)(13,55)(14,56)(15,53)(16,54)(17,65)(18,66)(19,68)(20,67)
(21,71)(22,72)(23,69)(24,70)(25,82)(26,81)(27,83)(28,84)(29,88)(30,87)(31,86)
(32,85)(33,74)(34,73)(35,75)(36,76)(37,80)(38,79)(39,78)(40,77)(41,90)(42,89)
(43,91)(44,92)(45,96)(46,95)(47,94)(48,93);
s3 := Sym(99)!(98,99);
s4 := Sym(99)!(97,98);
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, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 >;
to this polytope