Computing knot/link groups

I plugged this into SnapPy and got the following presentation:

Generators: a,b,c,d

Relators: abCBACADadcDAdabCBADadCDAdadcDAdabcBADadCDAdacabcBADadCBCbcDAdabCBACdcDadCDcabcBADadCBcbcDAd, abCBCbDAdacACADadBcbcDAd, abCBACdcDAdCDcDadCDADadcDAdabCBADadCDAdadcDAdCdcDadCDcabcBADadCBcbcDAd

(That is, four generators, three relators.) The link complement has volume approximately 33.331392948. Since the link is alternating and has no flypes, the diagram shown is minimal - thus the crossing number is 16. One more thing - the diagram has an involution about the central vertical line. You could mod out by this involution to get a smaller orbifold - there might be something known about the quotient...