Overview
- Group
- SmallGroup(384,18032)
- Rank
- 4
- Schläfli Type
- {3,4,8}
- Vertices, edges, …
- 6, 12, 32, 8
- Order of s0s1s2s3
- 24
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{3,4},{4,8|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
Covers minimal covers in bold
2-fold
3-fold
5-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 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);; s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(37,41)(38,42)(39,44)(40,43)(47,48)(49,53)(50,54)(51,56)(52,55)(59,60)(61,65)(62,66)(63,68)(64,67)(71,72)(73,77)(74,78)(75,80)(76,79)(83,84)(85,89)(86,90)(87,92)(88,91)(95,96);; s2 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,40)(26,39)(27,38)(28,37)(29,44)(30,43)(31,42)(32,41)(33,48)(34,47)(35,46)(36,45)(49,76)(50,75)(51,74)(52,73)(53,80)(54,79)(55,78)(56,77)(57,84)(58,83)(59,82)(60,81)(61,88)(62,87)(63,86)(64,85)(65,92)(66,91)(67,90)(68,89)(69,96)(70,95)(71,94)(72,93);; s3 := ( 1,49)( 2,50)( 3,51)( 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)(25,85)(26,86)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)(33,93)(34,94)(35,95)(36,96)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)(45,81)(46,82)(47,83)(48,84);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(96)!( 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); s1 := Sym(96)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(37,41)(38,42)(39,44)(40,43)(47,48)(49,53)(50,54)(51,56)(52,55)(59,60)(61,65)(62,66)(63,68)(64,67)(71,72)(73,77)(74,78)(75,80)(76,79)(83,84)(85,89)(86,90)(87,92)(88,91)(95,96); s2 := Sym(96)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,40)(26,39)(27,38)(28,37)(29,44)(30,43)(31,42)(32,41)(33,48)(34,47)(35,46)(36,45)(49,76)(50,75)(51,74)(52,73)(53,80)(54,79)(55,78)(56,77)(57,84)(58,83)(59,82)(60,81)(61,88)(62,87)(63,86)(64,85)(65,92)(66,91)(67,90)(68,89)(69,96)(70,95)(71,94)(72,93); s3 := Sym(96)!( 1,49)( 2,50)( 3,51)( 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)(25,85)(26,86)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)(33,93)(34,94)(35,95)(36,96)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)(45,81)(46,82)(47,83)(48,84); poly := sub<Sym(96)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.