  We present inelastic neutron scattering measurements of the antiferromagnetic
insulator CaMn$_2$Sb$_2$, which consists of corrugated honeycomb layers of Mn.
The dispersion of magnetic excitations has been measured along the H and L
directions in reciprocal space, with a maximum excitation energy of $\approx$
24 meV. These excitations are well described by spin waves in a Heisenberg
model, including first and second neighbor exchange interactions, J$_{1}$ and
J$_{2}$, in the Mn plane and also an exchange interaction between planes. The
determined ratio J$_{2}$/J$_{1}$ $\approx$ 1/6 suggests that CaMn$_2$Sb$_2$ is
the first example of a compound that lies very close to the mean field
tricritical point, known for the classical Heisenberg model on the honeycomb
lattice, where the N\'eel phase and two different spiral phases coexist. The
magnitude of the determined exchange interactions reveal a mean field ordering
temperature $\approx$ 4 times larger than the reported N\'eel temperature
T$_{N}$ = 85 K, suggesting significant frustration arising from proximity to
the tricritical point.
