  There is strong observational evidence that convective cores of
intermediate-mass and massive main-sequence stars are substantially larger than
standard stellar-evolution models predict. However, it is unclear what physical
processes cause this phenomenon or how to predict the extent and stratification
of stellar convective boundary layers. Convective penetration is a
thermal-time-scale process that is likely to be particularly relevant during
the slow evolution on the main sequence. We use our low-Mach-number
Seven-League Hydro (SLH) code to study this process in 2.5D and 3D geometries.
Starting with a chemically homogeneous model of a $15$ M$_\odot$ zero-age
main-sequence star, we construct a series of simulations with the luminosity
increased and opacity decreased by the same factor ranging from $10^3$ to
$10^6$. After reaching thermal equilibrium, all of our models show a clear
penetration layer. Its thickness becomes statistically constant in time and it
is shown to converge upon grid refinement. As the luminosity is decreased, the
penetration layer becomes nearly adiabatic with a steep transition to a
radiative stratification. This structure corresponds to the adiabatic ,,step
overshoot'' model often employed in stellar-evolution calculations. The
thickness of the penetration layer slowly decreases with decreasing luminosity.
Depending on how we extrapolate our 3D data to the actual luminosity of the
initial stellar model, we obtain penetration distances ranging from $0.09$ to
$0.44$ pressure scale heights, which are broadly compatible with observations.
