Borromean rings 6:3-02 AbAbAb (.1 = 6* or 623) are the origin of achiral alternating knots 8:1-07 A2bAbAb2 (.2.2 or 817), 10:1-020 A2bA2b2Ab2 (.2.2.2 0.2 0 or 1099), 10:1-022 A2b2AbA2b2 (2.2.2.2 or 10109), and of the link 8:3-04a Ab2AbA2b (.2:2 0 or 863), etc. In general, from AbAbAb the following families of achiral alternating KLs are derived
 

ApbAbAbp .p.p  ApbAqbqAbp .p.p.q 0.q 0 
AbpAbAp .p:p 0  ApbqArbrAqbp p.q.r.r.q.p 
ApbqAbAqbp p.q.q.p 

Achiral basic polyhedron AbAbAbAb (8*) is the origin of the following families of alternating achiral KLs: 
 
 
ApbAbAbAbp 8*p.p  ApbAbqAqbAbp 8*p.q:.q.p 
AbApbAbpAb  8*p:.p  ApbqArbAbrAqbp 8*p.q.r.r.q.p 
ApbqAbAbAqbp 8*p.q.q.p  ApbAqbrArbqAbp 8*p.q.q.p:r.r 
ApbAqbAbqAbp 8*.p:q.q:p 

In the same way it is possible to derive achiral alternating KLs from all achiral basic polyhedra (Ab)n for n ³ 5. 

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