  We obtain the exact physical characteristics of the triple-chain Ising model
on a torus with all possible multispin interactions invariant with respect to
rotation by the angle $2\pi / 3$. The exact value of the partition function in
a finite cyclically closed strip of length $L$, as well as the free energy,
internal energy, specific heat, magnetization, susceptibility, and entropy in
the thermodynamic limit at $L \to \infty$ are found by the transfer-matrix
method for the model. The spectrum of the transfer-matrix and the structure of
its eigenvectors are found. For two special cases - for the model with
multispin interactions of even number of spins and for the model with some
interactions of two, three, four and six spins, simplified expressions of the
mentioned physical characteristics are obtained; in the thermodynamic limit
they are expressed through the logarithm of the root of the quadratic equation.
For the model with multispin interactions of an even number of spins, a kind of
pair correlations in the thermodynamic limit is found, and it is shown that the
magnetization at zero magnetic field is equal to zero; the structure of the
ground states of the system is found and examples of their projections of
seven-dimensional space onto three-dimensional space and examples of
configurations corresponding to these ground states are given. The correlation
length is shown and its graphs are given. As special cases, we consider the
planar triangular model with all possible interactions, including, perhaps,
different triple interactions inside neighboring triangles, and the planar
model with nearest-neighbor, next nearest-neighbor, and plaquette interactions.
For them the main exact physical characteristics have been found. This allowed
us to obtain them for the planar gonihedric model as well.
