Basic graph theory

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:

A^pbAbAb^p	.p.p	A^pbA^qb^qAb^p	.p.p.q 0.q 0
Ab^pAbA^pb	.p:p 0	A^pb^qA^rb^rA^qb^p	p.q.r.r.q.p
A^pb^qAbA^qb^p	p.q.q.p

Achiral basic polyhedron AbAbAbAb (8^*) is the origin of the following families of alternating achiral KLs:

A^pbAbAbAb^p 8^*p.p A^pbAb^qA^qbAb^p 8^*p.q:.q.p

AbA^pbAb^pAb 8^*p:.p A^pb^qA^rbAb^rA^qb^p 8^*p.q.r.r.q.p

A^pb^qAbAbA^qb^p 8^*p.q.q.p A^pbA^qb^rA^rb^qAb^p 8^*p.q.q.p:r.r

A^pbA^qbAb^qAb^p 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.