  In this paper, we present a new model for Direction of Arrival (DOA)
estimation of sound sources based on an Icosahedral Convolutional Neural
Network (CNN) applied over SRP-PHAT power maps computed from the signals
received by a microphone array. This icosahedral CNN is equivariant to the 60
rotational symmetries of the icosahedron, which represent a good approximation
of the continuous space of spherical rotations, and can be implemented using
standard 2D convolutional layers, having a lower computational cost than most
of the spherical CNNs. In addition, instead of using fully connected layers
after the icosahedral convolutions, we propose a new soft-argmax function that
can be seen as a differentiable version of the argmax function and allows us to
solve the DOA estimation as a regression problem interpreting the output of the
convolutional layers as a probability distribution. We prove that using models
that fit the equivariances of the problem allows us to outperform other
state-of-the-art models with a lower computational cost and more robustness,
obtaining root mean square localization errors lower than 10{\deg} even in
scenarios with a reverberation time $T_{60}$ of 1.5 s.
