  We study the $O(N)^3$ symmetric quantum field theory of a bosonic tensor
$\phi^{abc}$ with sextic interactions. Its large $N$ limit is dominated by a
positive-definite operator, whose index structure has the topology of a prism.
We present a large $N$ solution of the model using Schwinger-Dyson equations to
sum the leading diagrams, finding that for $2.81 < d < 3$ and for $d<1.68$ the
spectrum of bilinear operators has no complex scaling dimensions. We also
develop perturbation theory in $3-\epsilon$ dimensions including eight $O(N)^3$
invariant operators necessary for the renormalizability. For sufficiently large
$N$, we find a "prismatic" fixed point of the renormalization group, where all
eight coupling constants are real. The large $N$ limit of the resulting
$\epsilon$ expansions of various operator dimensions agrees with the
Schwinger-Dyson equations. Furthermore, the $\epsilon$ expansion allows us to
calculate the $1/N$ corrections to operator dimensions. The prismatic fixed
point in $3-\epsilon$ dimensions survives down to $N\approx 53.65$, where it
merges with another fixed point and becomes complex. We also discuss the $d=1$
model where our approach gives a slightly negative scaling dimension for
$\phi$, while the spectrum of bilinear operators is free of complex dimensions.
