  The uniform Tur\'an density $\pi_{1}(F)$ of a $3$-uniform hypergraph $F$ is
the supremum over all $d$ for which there is an $F$-free hypergraph with the
property that every linearly sized subhypergraph with density at least $d$.
Determining $\pi_{1}(F)$ for given hypergraphs $F$ was suggested by Erd\H{o}s
and S\'os in 1980s. In particular, they raised the questions of determining
$\pi_{1}(K_4^{(3)-})$ and $\pi_{1}(K_4^{(3)})$. The former question was solved
recently in [Israel J. Math. 211 (2016), 349-366] and [J. Eur. Math. Soc. 20
(2018), 1139-1159], while the latter is still a major open problem. In addition
to $K_4^{(3)-}$, there are very few hypergraphs whose uniform Tur\'an density
has been determined.
  In this paper, we give a sufficient condition for $3$-uniform hypergraphs $F$
satisfying $\pi_{1}(F)=1/4$. In particular, currently all known $3$-uniform
hypergraphs whose uniform Tur\'an density is $1/4$, such as $K_4^{(3)-}$ and
the $3$-uniform hypergraphs $F^{\star}_5$ studied in [arXiv:2211.12747],
satisfy this condition. Moreover, we find some intriguing $3$-uniform
hypergraphs whose uniform Tur\'an density is also $1/4$.
