Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,4,3,2}

Atlas Canonical Name {8,4,3,2}*768

Overview

Group
SmallGroup(768,1089270)
Rank
5
Schläfli Type
{8,4,3,2}
Vertices, edges, …
8, 32, 12, 6, 2
Order of s0s1s2s3s4
24
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96);;
s1 := ( 1,51)( 2,52)( 3,49)( 4,50)( 5,55)( 6,56)( 7,53)( 8,54)( 9,59)(10,60)(11,57)(12,58)(13,63)(14,64)(15,61)(16,62)(17,67)(18,68)(19,65)(20,66)(21,71)(22,72)(23,69)(24,70)(25,87)(26,88)(27,85)(28,86)(29,91)(30,92)(31,89)(32,90)(33,95)(34,96)(35,93)(36,94)(37,75)(38,76)(39,73)(40,74)(41,79)(42,80)(43,77)(44,78)(45,83)(46,84)(47,81)(48,82);;
s2 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)(74,75)(77,81)(78,83)(79,82)(80,84)(86,87)(89,93)(90,95)(91,94)(92,96);;
s3 := ( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,21)(14,24)(15,23)(16,22)(18,20)(25,33)(26,36)(27,35)(28,34)(30,32)(37,45)(38,48)(39,47)(40,46)(42,44)(49,57)(50,60)(51,59)(52,58)(54,56)(61,69)(62,72)(63,71)(64,70)(66,68)(73,81)(74,84)(75,83)(76,82)(78,80)(85,93)(86,96)(87,95)(88,94)(90,92);;
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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(98)!(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96);
s1 := Sym(98)!( 1,51)( 2,52)( 3,49)( 4,50)( 5,55)( 6,56)( 7,53)( 8,54)( 9,59)(10,60)(11,57)(12,58)(13,63)(14,64)(15,61)(16,62)(17,67)(18,68)(19,65)(20,66)(21,71)(22,72)(23,69)(24,70)(25,87)(26,88)(27,85)(28,86)(29,91)(30,92)(31,89)(32,90)(33,95)(34,96)(35,93)(36,94)(37,75)(38,76)(39,73)(40,74)(41,79)(42,80)(43,77)(44,78)(45,83)(46,84)(47,81)(48,82);
s2 := Sym(98)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)(74,75)(77,81)(78,83)(79,82)(80,84)(86,87)(89,93)(90,95)(91,94)(92,96);
s3 := Sym(98)!( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(13,21)(14,24)(15,23)(16,22)(18,20)(25,33)(26,36)(27,35)(28,34)(30,32)(37,45)(38,48)(39,47)(40,46)(42,44)(49,57)(50,60)(51,59)(52,58)(54,56)(61,69)(62,72)(63,71)(64,70)(66,68)(73,81)(74,84)(75,83)(76,82)(78,80)(85,93)(86,96)(87,95)(88,94)(90,92);
s4 := Sym(98)!(97,98);
poly := sub<Sym(98)|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, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;