  We present the GEOMAX algorithm and its Python implementation for a two-step
compression of bispectrum measurements. The first step groups bispectra by the
geometric properties of their arguments; the second step then maximises the
Fisher information with respect to a chosen set of model parameters in each
group. The algorithm only requires the derivatives of the data vector with
respect to the parameters and a small number of mock data, producing an
effective, non-linear compression. By applying GEOMAX to bispectrum monopole
measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we
reduce the $68\%$ credible intervals for the inferred parameters
$\left(b_1,b_2,f,\sigma_8\right)$ by $\left(50.4\%,56.1\%,33.2\%,38.3\%\right)$
with respect to standard MCMC on the full data vector. We run the analysis and
comparison between compression methods over one hundred galaxy mocks to test
the statistical significance of the improvements. On average GEOMAX performs
$\sim15\%$ better than geometrical or maximal linear compression alone and is
consistent with being lossless. Given its flexibility, the GEOMAX approach has
the potential to optimally exploit three-point statistics of various
cosmological probes like weak lensing or line-intensity maps from current and
future cosmological data-sets such as DESI, Euclid, PFS and SKA.
