  CK Vul is the remnant of an energetic eruption known as Nova 1670 that is
thought to be caused by a stellar merger. The remnant is composed of (1) a
large hourglass nebula of recombining gas (of 71\arcsec size), very similar to
some classical planetary and pre-planetary nebulae (PPNe), and (2) of a much
smaller and cooler inner remnant prominent in millimeter-wave emission from
molecules. We investigate the three-dimensional spatio-kinematic structure of
both components. The analysis of the hourglass structure yields a revised
distance to the object of >2.6 kpc, at least 3.7 times greater than so far
assumed. At this distance, the stellar remnant has a bolometric luminosity >12
L$_{\odot}$ and is surrounded by molecular material of total mass >0.8
M$_{\odot}$ (the latter value has a large systematic uncertainty). We also
analyzed the architecture of the inner molecular nebula using ALMA observations
of rotational emission lines obtained at subarcsecond resolution. We find that
the distribution of neutral and ionized gas in the lobes can be reproduced by
several nested and incomplete shells or jets with different velocity fields and
varying orientations. The analysis indicates that the molecular remnant was
created in several ejection episodes, possibly involving an interacting binary
system. We calculated the linear momentum ($\approx$10$^{40}$ g cm s$^{-1}$)
and kinetic energy ($\approx$10$^{47}$ erg) of the CK Vul outflows and find
them within the limits typical for classical PPNe. Given the similarities of
the CK Vul outflows to PPNe, we suggest there may CK Vul analogs among wrongly
classified PPNe with low intrinsic luminosities, especially among PPNe with
post-red-giant-branch central stars.
